|
1-dimensional Lagrange element
|
|
2-dimensional Lagrange element
|
|
A priory estimate for penalised solution 1
|
|
A priory estimates for Galerkin solution 1
|
|
AS convergence vs convergence in pr 1
|
|
AS convergence vs convergence in pr 2
|
|
Abramowitz
|
|
Accelerated calculation of Gram matrix
|
|
Adapting GMRA to interval [0,1] section
|
|
Adapting MRA to the interval [0,1] section
|
|
Adapting dual wavelets to interval [0,1] section
|
|
Adapting scaling function to the interval [0,1] section
|
|
Adapting wavelet basis to arbitrary interval
|
|
Adapting wavelets to the interval [0,1] section
|
|
Adaptive approximation section
|
|
Adaptive time step for Black PDE section
|
|
Adjoint of surjection
|
|
Adjustment of scale
|
|
Affine alpha component
|
|
Affine beta component
|
|
Affine boundary conditions
|
|
Affine characteristic function 1
|
|
Affine characteristic function 2
|
|
Affine hull
|
|
Affine set
|
|
Affine_equation_ab
|
|
Affine_equation_section
|
|
Affinity_pq
|
|
Algebraic tensor product of Hilbert spaces
|
|
Almost sure convergence
|
|
Almost sure convergence 2
|
|
AlphaK and BetaK 1
|
|
AlphaK and BetaK 2
|
|
Alternating_boundary
|
|
Alternating_boundary1
|
|
Alternating_boundary2
|
|
Alternating_directions1
|
|
Alternating_directions2
|
|
Analytic preconditioner for Black equation
|
|
Analytical preconditioner derived from asymptotic decomposition in time
|
|
Analytical solution for mean reverting equation
|
|
Andersen1998
|
|
Andersen1999
|
|
Andersen2001
|
|
Andersen2005
|
|
Andersen2007
|
|
AndersenOnLine
|
|
Antonov2006
|
|
Antonov2006a
|
|
Antonov2007
|
|
Approximate toy problem
|
|
Approximation and detail operators
|
|
Approximation and detail operators 2
|
|
Approximation and detail operators 3
|
|
Approximation and detail operators 4
|
|
Approximation and detail operators section
|
|
Approximation by smooth functions
|
|
Approximation in Nitsche norm
|
|
Arzela-Ascoli compactness criterion
|
|
Asian PDE
|
|
Assumption of coercivity 1
|
|
Asymptotic expansion for Black equation section
|
|
Asymptotic expansion of Laplace integral
|
|
Asymptotic expansion of Laplace integral section
|
|
Asymptotic expansions chapter
|
|
Asymptotic of generic Laplace integral
|
|
Asymptotic of integral with Gaussian kernel
|
|
Avellaneda1995
|
|
AvellanedaLawrence
|
|
Average difference lemma
|
|
Averaged Taylor polynomial
|
|
Averaged Taylor polynomial section
|
|
Backward Euler convergence 2
|
|
Backward Euler problem
|
|
Backward Kolmogorov PDE
|
|
Backward Kolmogorov PDE setup
|
|
Backward Kolmogorov equation
|
|
Backward Kolmogorov for Feller process
|
|
Backward Kolmogorov for discounted payoff
|
|
Backward Kolmogorov for running payoff
|
|
Backward Kolmogorov generator
|
|
Backward Kolmogorov with localization
|
|
Backward Kolmogorov with running payoff
|
|
Backward discontinuous Galerkin time-discretization
|
|
Backward induction
|
|
Backward propagator
|
|
Backward_equation_for_jump_diffusion
|
|
Backward_equation_section
|
|
Banach fixed point theorem
|
|
Banach space
|
|
Basic Math II part
|
|
Basic coherence condition
|
|
Basic existence of incomplete market pricing
|
|
Basic existence result
|
|
Basic properties of Fourier transform
|
|
Basic properties of conditional expectation
|
|
Basic properties of propagator 1
|
|
Basic properties of propagator 2
|
|
Basic property of orthogonal polynomials
|
|
Basis in Hilbert space
|
|
Basket credt derivative section
|
|
Bayes_formula
|
|
Bayesian_technique
|
|
Baysian_statistics_section
|
|
Bellman equation section
|
|
Bensoussan
|
|
Bernstein inequality for wavelets
|
|
Bertoin
|
|
Bertsekas2003
|
|
Bessel equality
|
|
BetaK separation of random walk
|
|
Bielecki
|
|
Bilinear form B
|
|
Bilinear form B 2
|
|
Biorthogonal QMF conditions
|
|
Biorthogonal QMF property 1
|
|
Biorthogonal QMF property 2
|
|
Biorthogonal scaling functions
|
|
Biorthogonal symmetry 1
|
|
Biorthogonal symmetry 2
|
|
Biorthogonal symmetry 3
|
|
Biorthogonality
|
|
Biorthogonality criteria 1
|
|
Black Scholes formula
|
|
Black Scholes property 1
|
|
Black final payoff plot
|
|
Black solution plot
|
|
BlackScholesUndiscountedCall
|
|
Bond SDE
|
|
Boost
|
|
Borel measurable function
|
|
Borell-Cantelli's lemma, part 1
|
|
Borell-Cantelli's lemma, part 2
|
|
Boundary elliptic regularity
|
|
Boundary_trick
|
|
Boundedness of adjoint of surjection
|
|
Boundedness of interpolation operator
|
|
Boundedness of surjection
|
|
Bounds of interpolation error section
|
|
Box-Muller procedure
|
|
Bramble-Hilbert lemma
|
|
Brenner
|
|
Brownian_motion
|
|
C to W1p estimate
|
|
C0gamma vs W1p estimate
|
|
CLT
|
|
Calamos
|
|
Calculation of approximation spaces chapter
|
|
Calculation of approximation spaces in one dimension. Take two.
|
|
Calculation of biorthogonal wavelets section
|
|
Calculation of boundary scaling functions
|
|
Calculation of boundary scaling functions section
|
|
Calculation of boundary wavelets
|
|
Calculation of partial sums
|
|
Calculation of partial sums in parallel section
|
|
Calculation of scalar product in N dim
|
|
Calculation of scaling functions section
|
|
Calculation of w1 for a positive section
|
|
Calculation of w2 for a positive section
|
|
Calculation of w3 for a positive section
|
|
Calculational Linear Algebra chapter
|
|
Calculus behind the PiecewisePoly project section
|
|
Calculus behind the poly module section
|
|
Caratheodory theorem
|
|
Caratheodory theorem remark figure
|
|
CarrMadan1998
|
|
CarrMadan1999
|
|
CarrMadan2000
|
|
CarrWu2002
|
|
CarrWu2002a
|
|
CarrWu2006
|
|
CarrWu2006a
|
|
Cascade algorithm
|
|
Casella
|
|
Cauchy inequality
|
|
Cauchy inequality for scalar product 1
|
|
Cauchy inequality for scalar product 2
|
|
Cauchy inequality for scalar product section
|
|
Cauchy inequality with epsilon
|
|
Central limit theorem
|
|
Central limit theorem (CLT) II section
|
|
Cg to W1p estimate
|
|
Ch.f. of a sum
|
|
Chain_rule
|
|
Change of numeraire kernel
|
|
Change_of_Brownian_motion
|
|
Change_of_drift_recipe
|
|
Change_of_drift_recipe_1
|
|
Change_of_measure_definition_section
|
|
Change_of_measure_recipe_section
|
|
Change_of_numeraire_definition_section
|
|
Change_of_numeraire_recipe_section
|
|
Changing scale of wavelet basis
|
|
Characterisation of H-tilde spaces
|
|
Characteristic exponent of a pm
|
|
Characteristic function chapter
|
|
Characteristic measure of Poisson point process
|
|
Chebyshev inequality
|
|
Chebyshev polynomials
|
|
Chebyshev polynomials calculation
|
|
Chebyshev polynomials orthogonality
|
|
Chebyshev polynomials section
|
|
Cherny2006
|
|
Chf of entrance time 1
|
|
Chi squared distribution section
|
|
Choice of interval
|
|
Choosing probing functions section
|
|
Chung
|
|
Chunkiness parameter
|
|
Class D_T
|
|
Closedness and recession figure
|
|
Closeness and lower semicontinuity
|
|
Coefficients a
|
|
Coefficients of quadrature rule
|
|
Cohen
|
|
Coherent measure
|
|
Common shape identification
|
|
Common_application_of_change_of_measure
|
|
Compactly supported scaling function
|
|
Compactly supported smooth biorthogonal wavelets section
|
|
Complementary slackness
|
|
Complete measure space
|
|
Complete normed space
|
|
Complete tensor product of Hilbert spaces
|
|
Completion of measure via addition of null sets
|
|
Condition number
|
|
Conditional expectation
|
|
Conditional probability chapter
|
|
Conditionally_independent_defaults
|
|
Conjugate directions
|
|
Conjugate duality theorem
|
|
Conjugate gradient residue selection
|
|
Conjugate gradients
|
|
Connection between SLA and minimization
|
|
Constant finite element
|
|
Constraint qualification 1
|
|
Constraint qualification 2
|
|
Constraint qualification 3
|
|
Constraint qualification 4
|
|
Constraint qualification 5
|
|
Constructing dual GMRA on 01 with boundary conditions section
|
|
Constructing maximum summary
|
|
Construction of MRA and wavelets on half line or an interval section
|
|
Construction of MRA section
|
|
Construction of approximation spaces section
|
|
Construction of generic Levy process
|
|
Construction of symmetric biorthogonal wavelets
|
|
Continuity lemma
|
|
Continuity point
|
|
Convergence in Lp and in probability 1
|
|
Convergence in Lp and in probability 2
|
|
Convergence lemma for family of complex numbers
|
|
Convergence of cascade procedure section
|
|
Convergence of conjugate gradient method
|
|
Convergence of discontinuous Galerkin technique
|
|
Convergence of finite elements for generic parabolic operator section
|
|
Convergence of modified cascade procedure section
|
|
Convergence of pm and chf 1
|
|
Convergence of pm and chf 2
|
|
Convergence of product
|
|
Convergence theorem for martingales
|
|
Conversion of representations
|
|
Convex Hull Cone Relative Interior
|
|
Convex and proper function
|
|
Convex function picture
|
|
Convex homogenous function property
|
|
Convex hull
|
|
Convex set
|
|
Convexity of partial minimum
|
|
Convolution and smoothing section
|
|
Convolution of polynomials 1
|
|
Convolution of polynomials 2
|
|
Convolution of polynomials 3
|
|
Convolution of polynomials 4
|
|
Copula_calculation_for_CDO
|
|
Corrected difference 2 figure
|
|
Corrected difference figure
|
|
Crank-Nicolson convergence for heat equation
|
|
Crank-Nicolson problem for heat equation
|
|
Credit risk figure 1
|
|
Credit risk figure 2
|
|
Credit risk figure 3
|
|
Credit_default_swap_section
|
|
Criteria of positive definiteness
|
|
Crossing points figure 1
|
|
Crossing points figure 2
|
|
Crossing points figure 3
|
|
Crossing theorem 1
|
|
Crossing theorem 2
|
|
Crossing theorem 2 figure
|
|
Crudification of piecewise-quadratic representation
|
|
Crudification operator
|
|
Crudification operator 2
|
|
Cuda and python section
|
|
Currency exchange section
|
|
Currency_change_of_numeraire_recipe
|
|
Cutoff function
|
|
DHE with term structure
|
|
Data Analysis part
|
|
Daubechies1992
|
|
Decomposition of a convex set
|
|
Decomposition of payoff function in one dimension section
|
|
Definition of A_i
|
|
Definition of Epsilon
|
|
Definition of Galerkin basis 1
|
|
Definition of K0
|
|
Definition of K1
|
|
Definition of P_i
|
|
Definition of Q_i
|
|
Definition of conditional probability section
|
|
Definition of g_k
|
|
Definition of the Poisson process
|
|
Definition_of_change_of_measure
|
|
Definitions and the main convergence theorem section
|
|
Delta hedging
|
|
Delta_hedging_with_predictable_jump_section
|
|
Derivative vs scale
|
|
Deterministic optimal control problem section
|
|
Diagonal preconditioner section
|
|
Difference figure
|
|
Differential inequality 1
|
|
Differential inequality 2
|
|
Differentiating call with respect to maturity 1
|
|
Differentiating call with respect to maturity 2
|
|
Differentiation of asymptotic power series
|
|
Dimension mismatch
|
|
Dimension of tensor product
|
|
Dirac delta function
|
|
Direct Fourier transform
|
|
Direction of recession figure
|
|
Directional derivative
|
|
Directions of recession
|
|
Dirichlet problem for generic parabolic operator
|
|
Discontinuous Galerkin time-discretization
|
|
Discrete wavelet transform section
|
|
Discrete wavelet transform setup
|
|
Discretization for backward Kolmogorov equation section
|
|
Discretization with respect to time parameter section
|
|
Displaced Heston equations
|
|
Displaced Heston equations chapter
|
|
Displaced diffusion section
|
|
Dissipation property of Feller process
|
|
Distribution density via Call
|
|
Distribution of Poisson process section
|
|
Dominated convergence theorem
|
|
Dual GMRA
|
|
Dual Sobolev spaces section
|
|
Dual basis
|
|
Dual feasibility
|
|
Dual frame
|
|
Dual problem
|
|
Dual space
|
|
Dual wavelets
|
|
Dual wavelets properties
|
|
Dual wavelets section
|
|
Duality gap and geometric multipliers
|
|
Duality picture 1
|
|
Duality picture 2
|
|
Duffie1999
|
|
Edwards
|
|
Egorov theorem
|
|
Eigenfunctions of Laplacian
|
|
Eigenvalues of compact symmetric operator
|
|
Eigenvalues of symmetric elliptic operator
|
|
Elementary CLT
|
|
Elementary definitions of wavelet analysis section
|
|
Elliptic Dirichlet problem
|
|
Elliptic PDE section
|
|
Elliptic Ritz projection
|
|
Elliptic alternative 1
|
|
Elliptic alternative 2
|
|
Elliptic boundedness of inverse
|
|
Elliptic differential operator
|
|
Elliptic regularity for Poisson equation
|
|
Elliptic regularity section
|
|
Embedding of dual Sobolev space
|
|
Energy approximation
|
|
Energy estimate 2
|
|
Energy estimates for the Galerkin approximate solution
|
|
Energy estimates for the bilinear form B
|
|
Equivalence of AS and PR convergence for series
|
|
Equivalence of toy problems
|
|
Equivalent definitions of vague convergence
|
|
Equivalent sequences of rv
|
|
Erdelyi
|
|
Error and residual
|
|
Error and residual 2
|
|
Estimate for K0
|
|
Estimate for K1 one
|
|
Estimate for K1 two
|
|
Estimate of interpolation error
|
|
Estimate of interpolation error 2
|
|
Estimate of interpolation error 3
|
|
Estimate of mean by probability series
|
|
Estimation of averaged Taylor polynomial
|
|
Euler Lagrange equation
|
|
Evaluating matrix R section
|
|
Evans
|
|
Eventuality of random walk
|
|
Evolution figure
|
|
Evolution of u
|
|
Evolution of y
|
|
Evolution with penalty term
|
|
Evolution_equation
|
|
Evolutionary penalised problem
|
|
Evolutionary variational inequalities section
|
|
Evolutionary variational inequality problem
|
|
Example Black equation parameters section
|
|
Example Black problem
|
|
Example approximate problem
|
|
Example stochastic elliptic problem
|
|
Example strong Black problem
|
|
Example strong Black problem 2
|
|
Example strong elliptic problem
|
|
Example weak elliptic problem
|
|
Existence and uniqueness for evolutionary problem
|
|
Existence and uniqueness for non-coercive stationary problem.
|
|
Existence and uniqueness for penalised problem
|
|
Existence and uniqueness for penalised problem 2
|
|
Existence and uniqueness for stationary problem
|
|
Existence for Galerkin approximation of stationary problem
|
|
Existence of Lagrange multipliers for equality constraints
|
|
Existence of Lebesgue measure
|
|
Existence of adapted wavelets
|
|
Existence of biorthogonal basis 1
|
|
Existence of biorthogonal compactly supported wavelets
|
|
Existence of conditional expectation
|
|
Existence of derivative via finite difference
|
|
Existence of incomplete market pricing
|
|
Existence of orthogonal polynomials
|
|
Existence of orthonormal wavelet bases 1
|
|
Existence of orthonormal wavelet bases 2
|
|
Existence of smooth compactly supported wavelets
|
|
Existence of subdifferential
|
|
Existence of wavelets with orthogonality across scales
|
|
Existence of weak solution for elliptic Dirichlet problem 1
|
|
Existence of weak solution for elliptic Dirichlet problem 2
|
|
Existence of weak solution for elliptic Dirichlet problem 3
|
|
Existence of weak solution for the parabolic Dirichlet problem
|
|
Existence of weak solution of the Heat equation
|
|
Existence of weak solution of the Poisson equation
|
|
Explicit_scheme
|
|
Exponential change
|
|
Extension of Borell-Cantelli lemma to random walk
|
|
Extension of measure to sigma algebra
|
|
Extension theorem
|
|
Extremal properties of orthogonal polynomials
|
|
Extreme points of polyhedral set 1
|
|
Extreme points of polyhedral set 2
|
|
FJ proof 1
|
|
FJ proof 2
|
|
FJ proof 3
|
|
Factorization1
|
|
Factorization2
|
|
Factorization3
|
|
Factorization4
|
|
Factorization5
|
|
Factorization6
|
|
Fair Variance vs Log contract
|
|
Farkas lemma
|
|
Fatou lemma
|
|
Feasible direction cone
|
|
Feller process
|
|
Feller process property 1
|
|
Filtration_definition_section
|
|
Finite QMF convergence
|
|
Finite difference basics
|
|
Finite difference basics section
|
|
Finite difference in Sobolev space
|
|
Finite difference schemes for heat equation section
|
|
Finite differences
|
|
Finite dimensional approximation 1
|
|
Finite dimensional approximation 2
|
|
Finite element
|
|
Finite element section
|
|
Finite elements chapter
|
|
Finite elements for Poisson equation with Dirichlet boundary conditions section
|
|
Finite space variable incomplete market
|
|
First order PDE
|
|
Form of Schwarz operator
|
|
Forward Kolmogorov equation for Ito process
|
|
Forward LIBOR
|
|
Forward and backward generators def
|
|
Forward and backward generators section
|
|
Forward propagator
|
|
Forward_Kolmogorov
|
|
Forward_exchange_rate
|
|
Fourier analysis in Hilbert space section
|
|
Fourier decomposition
|
|
Fourier series on unit interval
|
|
Fourier series section
|
|
Fourier transform
|
|
Fourier transform of convolution
|
|
Fourier transform of delta function section
|
|
Fourier transform of projection on span of translates
|
|
Fourier transform section
|
|
Frame formula 1
|
|
Frame norm
|
|
Frame operator
|
|
Frame property 1
|
|
Frame property 2
|
|
Frame property 3
|
|
Frame system
|
|
Fredholm alternative
|
|
Free boundary problem 1
|
|
Free boundary problem 2
|
|
Free boundary problem 2 summary
|
|
Friedrich lemma
|
|
Fritz John conditions
|
|
Fubini theorem
|
|
Function spaces section
|
|
Functional analysis chapter
|
|
Fundamental solution for ODE
|
|
GMRA Ries bases
|
|
Gagliardo-Nirenberg-Sobolev inequality
|
|
Galerkin approximation 1
|
|
Galerkin approximation 2
|
|
Galerkin approximation for parabolic Dirichlet problem section
|
|
Galerkin approximation of stationary problem
|
|
Galerkin coefficients
|
|
Galerkin convergence 1
|
|
Galerkin convergence 2
|
|
Galerkin convergence 3
|
|
Galerkin convergence 4
|
|
Galerkin convergence 5
|
|
Galerkin convergence 6
|
|
Galerkin problem
|
|
Gamma function primer
|
|
Gamma_distribution
|
|
Gatheral
|
|
Gauss-Hermite Intergration
|
|
Gaussian quadrature rule
|
|
Gautschi
|
|
Gelman
|
|
General_change_of_Brownian_motion
|
|
Generalized multiresolution analysis
|
|
Generator of Levy process
|
|
Generic Backward Kolmogorov
|
|
Generic Forward Kolmogorov
|
|
Generic parabolic PDE
|
|
Generic parabolic PDE problem
|
|
Generic parabolic PDE setup
|
|
Geometric multiplier
|
|
Geometric multiplier property
|
|
Gershgorin circle theorem
|
|
Gikhman
|
|
Girsanov theorem
|
|
Girsanov_kernel
|
|
Girsanov_theorem
|
|
Girsanov_theorem_A
|
|
Glasserman
|
|
Global approximation by smooth functions
|
|
Gram-Schmidt orthogonalization section
|
|
Green formula
|
|
Gyongy 2
|
|
Gyongy lemma section
|
|
H-tilde spaces
|
|
HI1
|
|
Haar functions section
|
|
Hahn decomposition theorem
|
|
Hamilton
|
|
Hankel determinants
|
|
Haug
|
|
Haykin
|
|
Heat equation weak formulation 1
|
|
Heat equation weak formulation 2
|
|
Heat equation with Dirichlet boundary condition
|
|
Heat equation with Neumann boundary condition
|
|
Heston approximation
|
|
Heston_equation_section
|
|
Heston_equations
|
|
Hewitt and Savage zero-or-one law
|
|
Hierarchical1
|
|
Hierarchical2
|
|
High order internal elliptic regularity
|
|
Higher degree of exactness
|
|
Holder inequality
|
|
Holder inequality 2
|
|
Holder inequality 3
|
|
Holospoudic
|
|
Holospoudic criteria
|
|
How does it extend to multiple dimensions section
|
|
Hull
|
|
Hyperplane representation
|
|
Hypothesis_testing_problem
|
|
IO criteria for AS convergence
|
|
Idea of Bayesian analysis section
|
|
Identification of nodal variables 1
|
|
Identification of nodal variables 2
|
|
Implementation for mean reverting equation section
|
|
Implementation tools II part
|
|
Implicit equation with penalty term
|
|
Implicit formulation of the penalty term section
|
|
Implicit spectrum
|
|
Implicit_scheme
|
|
Impossibility of backward induction section
|
|
Improving condition number
|
|
Incomplete Market 1
|
|
Incomplete Market 2
|
|
Incomplete market ask
|
|
Incomplete market bid
|
|
Independence of Poisson processes
|
|
Independency of pre-alpha and post-alpha fields
|
|
Independent process
|
|
Induced outer measure
|
|
Infimal convex function
|
|
Infimal convolution
|
|
Infimal convolution of support functions
|
|
Infinitely divisible pm
|
|
Infinitely often zero-or-one law
|
|
Instant smoothness of solution operator for PP 1
|
|
Int t_dW
|
|
Integral form of Taylor decomposition
|
|
Integral of scaling function
|
|
Integral of scaling function 2
|
|
Integral of wavelet
|
|
Integration by part for finite differences
|
|
Integration of fundamental solution for Black equation
|
|
Integration of polynomials
|
|
Interaction of approximation and detail operators with Fourier transform
|
|
Interaction of downsampling with Fourier transform
|
|
Interaction of tilde with Fourier transform
|
|
Interaction of upsampling with Fourier transform
|
|
Interpolant
|
|
Interpolated continuity
|
|
Interpolation inequality
|
|
Interpolation of Hilbert spaces section
|
|
Intersection of halfspaces
|
|
Intersection property
|
|
Invariant set
|
|
Inverse Fourier transform
|
|
Inversion of chf into df
|
|
Inversion of chf into pm 1
|
|
Inversion of chf into pm 2
|
|
Inversion_remark
|
|
Ito calculus
|
|
Ito calculus section
|
|
Ito formula 2
|
|
Ito isometry
|
|
Ito_derivative_of_product
|
|
Ito_formula
|
|
Jackson inequality for wavelets
|
|
Jackson inequality for wavelets 2
|
|
Jacobi matrix
|
|
Jensen inequality
|
|
Jordan decomposition theorem
|
|
Kalman_II_model
|
|
Kalman_filter_II_section
|
|
Karatzas1
|
|
Karatzas2
|
|
Known_Variance1
|
|
Known_Variance2
|
|
Kohn
|
|
Kolmogorov
|
|
Kolmogorov equations in general setting
|
|
Kolmogorov inequality for series 1
|
|
Kolmogorov inequality for series 2
|
|
Kolmogorov three series theorem
|
|
Kolmogorov zero-or-one law
|
|
Kolmogorov-Chapman equation
|
|
Krank_Nicolson
|
|
Krank_Nicolson_spectrum
|
|
Krein-Milman theorem
|
|
Kronecker summation lemma
|
|
LIBOR market model section
|
|
Lagrange interpolation formula
|
|
Lagrange interpolation formula 1
|
|
Lagrange multiplier
|
|
Lagrangian optimality
|
|
Lamberton
|
|
Laplace quadrature section
|
|
Laplace transform section
|
|
Laplace_bounds
|
|
Laplace_problem
|
|
Laplacian_Limits
|
|
Laplacian_Spectrum
|
|
Law of large number for iid rv with finite mean
|
|
Law of large numbers for independent rv
|
|
Lax-Milgram theorem
|
|
Lax_convergence_theorem
|
|
Lebesgue differentiation theorem
|
|
Lebesgue differentiation theorem section.
|
|
Lebesgue integral definition
|
|
Left and right derivatives
|
|
Lemarie
|
|
Levy process
|
|
Levy process chapter
|
|
Levy-Khintchine formula 1
|
|
Levy-Khintchine formula 2
|
|
Lewis
|
|
Liapounov CLT
|
|
Liapounov inequality
|
|
Libor
|
|
Libor2
|
|
Limit points
|
|
Limsup and liminf for sets
|
|
Lindeberg-Feller CLT
|
|
Lindeberg-Feller condition
|
|
Line segment principle
|
|
Linear equation
|
|
Linear independence from biorthogonality
|
|
Linear intersection result
|
|
Linear tensor product element
|
|
Linear transformation of random variables
|
|
Local approximation by smooth functions
|
|
Local minima of convex function
|
|
Local minimum of a sum
|
|
Localised integral
|
|
Localised scaling
|
|
Localised transport
|
|
Localization for mean reverting equation section
|
|
Localization for mean reverting equation summary
|
|
Localization section
|
|
Longstaff
|
|
Longstaff-Schwartz technique section
|
|
Lp interpolation
|
|
Lp vs W1p estimate
|
|
MMA numeraire
|
|
Magnitude of matrix Epsilon
|
|
Main properties of direction of recession
|
|
Main property of Fourier decomposition
|
|
Main property of Haar functions 1
|
|
Main property of basis in Hilbert space
|
|
Main property of convex function
|
|
Main property of crudification operator
|
|
Main_property_of_change_of_measure
|
|
Mallat
|
|
Manipulation of localized piecewise polynomial functions
|
|
Mapping of conditional expectation
|
|
Mapping of rv
|
|
Marchuk
|
|
MarkPr TargetEquation
|
|
MarkPr TargetEquations 2
|
|
MarkPr1 Beta
|
|
MarkPr1 Sigma
|
|
Market model section
|
|
Market_price_of_risk
|
|
Markov property
|
|
Markovian projection
|
|
Markovian projection on displaced diffusion section
|
|
Markovian projection section
|
|
Martingale definition
|
|
Martingale property of Feller process
|
|
Mathematica Test 1
|
|
Mathematica Test 1a
|
|
Mathematica Test 2
|
|
Mathematica Test 3
|
|
Matrix Lambda
|
|
Matrix V
|
|
Matrix of discontinuous Galerkin
|
|
Maximal dimension 1
|
|
Maximal inequality for martingales
|
|
Maximal_likelihood_section
|
|
Maximum of random walk
|
|
Mean reversion 0
|
|
Mean reversion 1
|
|
Mean reversion 2
|
|
Mean reversion 3
|
|
Mean reversion 4
|
|
Mean reversion 5
|
|
Mean reverting equation section
|
|
Mean reverting free boundary problem
|
|
Mean reverting free boundary problem 2
|
|
Mean reverting problem
|
|
Mean reverting problem 2
|
|
Mean reverting solution
|
|
Measurable set
|
|
Measurable space
|
|
Mercurio
|
|
Method of conjugate directions section
|
|
Method of conjugate gradients section
|
|
Method of steepest descent section
|
|
Meyer
|
|
Min common and max crossing point section
|
|
Minimax equality
|
|
Minimax lemma 1
|
|
Minimax lemma 2
|
|
Minimax theorem
|
|
Minimax theorem 1
|
|
Minimization with equality constraints
|
|
Minimum norm optimality of Chebyshev polynomials
|
|
Minimum of a convex function
|
|
Minimum of a smooth function
|
|
Minkowski-Weyl representation
|
|
Minkowski-Weyl theorem
|
|
Minmax_theorem
|
|
Mix of backward induction and penalty term approaches I. Implementation and results section
|
|
Mix of backward induction and penalty term approaches II section
|
|
Mix of backward induction and penalty term approaches section
|
|
Mix2 figure 1
|
|
Mix2 figure 2
|
|
Mix2 figure 3
|
|
Mix2 figure 4
|
|
Modified cascade procedure
|
|
Mollifier for a ball 1
|
|
Mollifier for a ball 2
|
|
Monotonicity of solution of stationary problem
|
|
Morrey inequality
|
|
Multidimensional Gyongy lemma
|
|
Multidimensional backward Kolmogorov equation
|
|
Multiplication of polynomials
|
|
Multiresolution analysis
|
|
Multiresolution analysis section
|
|
Musiela
|
|
N-dim test 1
|
|
Necessary and sufficient optimality conditions
|
|
Nielsen
|
|
Nitsche bilinear form
|
|
Nitsche form energy estimates
|
|
No drift Black Scholes
|
|
Non emptiness of relative interior
|
|
Non-coercivity assumption 1
|
|
Nondecreasing ratio
|
|
Nonvertical separation
|
|
Nonvertical separation figure
|
|
Norm
|
|
Normal cone
|
|
Normal cone figure 1
|
|
Normal distribution with unknown parameters 1
|
|
Normal distribution with unknown parameters 2
|
|
Normal_variable
|
|
Notation W_d
|
|
Numerical
|
|
Numerical analysis part
|
|
O symbols
|
|
OST property 0
|
|
OST property 1
|
|
OST property 2
|
|
OST property 3
|
|
ObjectBrowser1
|
|
ObjectBrowser2
|
|
ObjectBrowser3
|
|
Oksendal
|
|
One dime payoff residue figure
|
|
One dimensional problems chapter
|
|
Operations on sets and logical statements
|
|
Operator L
|
|
Operator L 2
|
|
Optimal stopping
|
|
Optimal stopping time problem section
|
|
Optimal strategy with accrual
|
|
Optimal utility section delta hedging
|
|
Optimality for smooth function figure 1
|
|
Optimality for smooth function figure 2
|
|
Optional random variable
|
|
Optional sampling theorem
|
|
Order of summation 0
|
|
Order of summation 1
|
|
Order of summation 2
|
|
Order of summation 3
|
|
Order of summation 4
|
|
Order of summation 5
|
|
Orthogonal L2 projection
|
|
Orthogonal polynomials
|
|
Orthogonal_normal_variables
|
|
Orthogonality of residues
|
|
Orthogonality of residues 2
|
|
Orthonormal system of translates def
|
|
Orthonormal system of translates section
|
|
Orthonormal wavelet bases section
|
|
Orthonormal wavelet basis
|
|
OswaldOnline
|
|
Outer measure
|
|
Parabolic Dirichlet problem
|
|
Parabolic PDE section
|
|
Parabolic differential operator
|
|
Parabolic problem with nonsmooth initial condition
|
|
Parabolic regularity 1
|
|
Parabolic regularity 2
|
|
Parabolic regularity for heat equation
|
|
Parabolic regularity section
|
|
Parallel subspace correction method section
|
|
Parallel subspace preconditioner
|
|
Parallel subspace preconditioner property
|
|
Parameter averaging
|
|
Parameter averaging section
|
|
Parameter d
|
|
Parseval equality
|
|
Partial inversion lemma
|
|
Partial inversion lemma 2
|
|
Partial minimization result
|
|
Partial solution
|
|
Partial summation in parallel
|
|
Partially inverted problem
|
|
Partially inverted semidiscrete parabolic problem
|
|
Partially inverted semidiscrete parabolic problem 1
|
|
Partition of unity definition
|
|
Pathwise differentiation
|
|
Payoff figure
|
|
Penalisation error
|
|
Penalised evolutionary problem section
|
|
Penalized mean reverting problem
|
|
Penalized problem
|
|
Penalized problem for mean reverting equation section
|
|
Permutable set
|
|
Permutation
|
|
Pervasive idea of recursive calculation section
|
|
PetersdorffSchwab
|
|
Piecewise Quadratic Polynomial picture
|
|
Piecewise convolution
|
|
Piecewise linear MRA section
|
|
Piecewise polynomial representation
|
|
Piecewise polynomials in parallel
|
|
Piecewise polynomials section
|
|
Piterbarg2003
|
|
Piterbarg2003a
|
|
Piterbarg2003b
|
|
Piterbarg2005
|
|
Piterbarg2005a
|
|
Piterbarg2006
|
|
Pm vs chf estimate
|
|
Poincare inequality
|
|
Poincare inequality for a ball
|
|
Poisson equation weak formulation 1
|
|
Poisson equation weak formulation 2
|
|
Poisson equation with Dirichlet boundary condition
|
|
Poisson formula for delta function
|
|
Poisson formula section
|
|
Poisson point process
|
|
Poisson point process section
|
|
Poisson process chapter
|
|
Poisson property 1
|
|
Poisson property 1a
|
|
Poisson property 2
|
|
Poisson property 3
|
|
Polar cone definition
|
|
Polar cone properties
|
|
Polar cone theorem
|
|
Polar polyhedral cone
|
|
Polyhedral function
|
|
Positive definite inner product
|
|
Possible value of random walk
|
|
Post-alpha process
|
|
Pre-alpha field
|
|
Precompactness of a tight sequence of pm
|
|
Preconditioner for Black equation in case q=1 section
|
|
Preconditioning section
|
|
Preliminary reduction
|
|
Preliminary reduction 2
|
|
Preservation of closeness result
|
|
Preservation of convexity
|
|
Preservation of stationary measure
|
|
Primal feasibility
|
|
Primal problem
|
|
Principal intersection result
|
|
Probability based criteria for AS convergence
|
|
Projection permuation
|
|
Projection theorem
|
|
Proof of existence for stationary problem section
|
|
Propagator and transitional probability
|
|
Proper separation 1
|
|
Proper separation 2
|
|
Properties of Feller resolvent 1
|
|
Properties of Feller resolvent 2
|
|
Properties of Feller resolvent 3
|
|
Properties of Poisson point process
|
|
Properties of Schwarz operator
|
|
Properties of averaged Taylor polynomial
|
|
Properties of dual frame
|
|
Properties of frame operator
|
|
Properties of interpolant
|
|
Properties of left and right derivative
|
|
Properties of mollifiers
|
|
Properties of sequences h and g
|
|
Properties of sequences h and g section
|
|
Properties of solution operator
|
|
Properties of solution operator 2
|
|
Properties of spline functions
|
|
Properties of subgradient
|
|
Property of equivalent sequences of rv
|
|
Property of scale and transport 1
|
|
Property of scale and transport 2
|
|
Property of scale and transport 3
|
|
Property of scale and transport 4
|
|
Property of scale and transport 5
|
|
Property of scale and transport 6
|
|
Property of scale and transport 7
|
|
Property of transport 1
|
|
Property of transport 2
|
|
Pseudonormality
|
|
Python to R Communicator section
|
|
Python utilities section
|
|
QMF conditions
|
|
QMF property 1
|
|
QMF property 2
|
|
QMF section
|
|
Quadratic form minimum
|
|
Quadratic intersection result
|
|
Quadratic piecewise interpolation
|
|
Quadratic piecewise interpolation 2
|
|
Quadratic polynomials 1
|
|
Quadratic polynomials 2
|
|
Quadratic polynomials 3
|
|
Quadratic polynomials 4
|
|
Quadratic polynomials 5
|
|
Quadrature rule
|
|
Quadrature rule 1
|
|
Radon-Nikodym theorem
|
|
Random walk
|
|
Random walk space
|
|
Random walk space approximation
|
|
Real valued random variable
|
|
Rebalancing wavelet basis problem
|
|
Rebalancing wavelet basis section
|
|
Rebonato
|
|
Recession cone of intersection
|
|
Recession cone of inverse image
|
|
Recovering MRA from auxilliary function 1
|
|
Recovering scaling function from auxilliary function section
|
|
Recurrence lemma 1
|
|
Recurrence lemma 2
|
|
Recurrence result 1
|
|
Recurrence result 2
|
|
Recurrent value of random walk
|
|
Recursive calculation
|
|
Recursive equation
|
|
Recursive relationships for wavelet section
|
|
Recursive relationships for wavelet transform
|
|
Reduction of Black equation
|
|
Reduction scheme 1
|
|
Reduction scheme 2
|
|
Reduction to system of linear algebraic equations for Black PDE section
|
|
Reduction to system of linear algebraic equations for mean reverting equation section
|
|
Reduction to system of linear algebraic equations for q=1
|
|
Reduction to system of linear algebraic equations for q=1 section
|
|
Reduction to system of linear algebraic equations for q=1 summary
|
|
Reduction to system of linear algebraic equations section
|
|
Reduction to system of linear algebraic equations summary
|
|
Reduction to well conditioned form section
|
|
Reflection principle picture
|
|
Reflection_principle
|
|
Regularity of a set
|
|
Relative interior figure
|
|
Rellich-Kondrachov compactness theorem
|
|
Remainder bound 1
|
|
Remainder of averaged Taylor polynomial
|
|
Remainder of averaged Taylor polynomial 2
|
|
Remainder of averaged Taylor polynomial 3
|
|
Remark on stability of financial problems
|
|
Remote event
|
|
Remote field
|
|
Removing stiffness from penalized equation section
|
|
Representation of dual Sobolev space
|
|
Representation of solution for elliptic PDE using stochastic process section
|
|
Reproduction of polynomials 1
|
|
Reproduction of polynomials 2
|
|
Reproduction of polynomials 3
|
|
Reproduction of polynomials 4
|
|
Resolution structure for adapted scale functions
|
|
Resolvent of Feller process
|
|
Restricted linear independence
|
|
Review of variational inequalities in maximization case section
|
|
RevuzYor
|
|
Ricatti_equation_section
|
|
Riesz basis
|
|
Riesz basis condition
|
|
Riesz frame
|
|
Riesz potential bound 1
|
|
Riesz potential bound 2
|
|
Riesz property
|
|
Riesz representation theorem
|
|
Risk neutral Brownian motion
|
|
Risk neutral measure via Girsanov section
|
|
Risk_neutral_pricing
|
|
Risky_annuity
|
|
Ritz projection convergence 1
|
|
Rockafellar
|
|
Royden
|
|
SDE_X
|
|
SDE_X_p
|
|
Saddle point defining property
|
|
Saddle point result 1
|
|
Saddle point result 2
|
|
Saddle point theorem
|
|
Same grid reduction
|
|
Saturated measure space
|
|
Scalar product in N dimensions
|
|
Scalar product in N-dimensions Test case 2
|
|
Scale and transport operators
|
|
Scale and transport operators 2
|
|
Scale of polynomial
|
|
Scaling equation
|
|
Scaling equation 2
|
|
Scaling equation 3
|
|
Scaling equation 4
|
|
Scaling equation 5
|
|
Scaling equation for wavelet section
|
|
Scaling equation section
|
|
Scaling filter and auxiliary function
|
|
Schewchuk
|
|
Schwartz space
|
|
Schwarz operator
|
|
Second derivative localization
|
|
Second order internal elliptic regularity
|
|
Self financing strategy
|
|
Semi-orthogonal wavelet bases section
|
|
Senior_tranche_loss
|
|
Separable and dense set
|
|
Separating hyperplane theorem
|
|
Shift
|
|
Shift and sampling operators
|
|
Shifted Fourier transform equality
|
|
Shreve
|
|
ShreveOnLine
|
|
Sigma algebra
|
|
Sigma finite set
|
|
Simple function definition
|
|
Simple law of large numbers
|
|
Simplistic_copula
|
|
Sklar_theorem_1
|
|
Sklar_theorem_2
|
|
Smooth compactly supported wavelets section
|
|
Smooth optimization problem
|
|
Smooth version of the penalty term section
|
|
Smoothness of compactly supported wavelets with vanishing moments
|
|
Smoothness of compactly supported wavelets with vanishing moments section
|
|
Sobolev conjugate
|
|
Sobolev inequality
|
|
Sobolev inequality 2
|
|
Sobolev space definition
|
|
Sobolev spaces in N dim as tensor products
|
|
Sobolev spaces section
|
|
Sobolev spaces with dominating mixed derivative
|
|
Solution operator for PP with nonsmooth IC
|
|
Solution operator for elliptic problem
|
|
Solution operator for generic elliptic problem
|
|
Solving N-dimensional PDEs section
|
|
Solving equation with implicit penalty term section
|
|
Solving one dimensional Black PDE section
|
|
Solving one dimensional mean reverting equation section
|
|
Space splitting setup
|
|
Sparse tensor product
|
|
Sparse tensor product approximation 1
|
|
Sparse tensor product approximation 2
|
|
Sparse tensor product definition section
|
|
Sparse tensor product section
|
|
Sparse tensor product setup
|
|
Spectral mapping theorem
|
|
Spectral_mapping
|
|
Spectrum of compact operator
|
|
Spitzer identity
|
|
Spline functions definition
|
|
Spline functions section
|
|
Stability of general evolution equation
|
|
Stability of one-dim heat equation schemes section
|
|
Stability of splitting for Sobolev spaces with dominating mixed derivative
|
|
Stability of splitting for tensor product of Sobolev spaces
|
|
Stability of wavelet splitting 1
|
|
Stability of wavelet splitting section
|
|
Stable space splittings section
|
|
Stable splitting
|
|
Standard mollifier definition
|
|
Standard_normal_variable
|
|
Star shaped set
|
|
Starting scaling function
|
|
Stationary independent increments
|
|
Stationary penalised problem
|
|
Stationary variational inequality problem
|
|
Steepest descent
|
|
Stochastic optimal control section
|
|
Stochastic optimization in one dimension chapter
|
|
Stochastic optimization over wavelet basis section
|
|
Stochastic process
|
|
Stregthened Cauchy-Schwartz inequality
|
|
Stress tests
|
|
Strict hyperplane separation 1
|
|
Strict hyperplane separation 2
|
|
Strong formulation of evolutionary problem
|
|
Strong formulation of stationary problem
|
|
Strong law of large numbers for iid rv
|
|
Strong law of large numbers for mean zero
|
|
Strong mean reverting problem
|
|
Strong mean reverting problem 2
|
|
Structure of recurrent values
|
|
Subgradient
|
|
Subgradient and subdifferential
|
|
Subordination
|
|
Subprobability measure
|
|
Subspace bases
|
|
Sufficient conditions for vanishing moments
|
|
Sufficient conditions for vanishing moments 2
|
|
Sufficient statistics for normal sample section
|
|
Sufficiently fine scale
|
|
Sufficiently fine scale 2
|
|
Suitable_numeraire
|
|
Summary for Black equation in case q=1
|
|
Summary for Black equation in case q=1 section
|
|
Summary for Black equation in case q=1, any time interval
|
|
Summary for Black equation in case q=1, inverted matrix
|
|
Summary for mean reverting equation in case q=1
|
|
Support function
|
|
Support of scaling function
|
|
Supporting hyperplane theorem
|
|
Sveshnikov
|
|
Swap rate
|
|
Symmetric biorthogonal wavelets section
|
|
Symmetric principal part
|
|
Symmetrization section
|
|
T-forward probability measure
|
|
Tangent cone
|
|
Tangent cone 2
|
|
Tangent cone 3
|
|
Tangent cone 4
|
|
Tangent cone figure 1
|
|
Tangent cone figure 2
|
|
Tavakoli
|
|
Taylor decomposition in Peano form
|
|
Taylor decomposition in Schlomilch, Lagrange and Cauchy forms
|
|
Taylor polynomial
|
|
Tensor product of Hilbert spaces section
|
|
Tensor product of bounded operators
|
|
Tensor product of function spaces
|
|
Tensor product properties 1
|
|
Tensor product properties 2
|
|
Tensor product splitting
|
|
Thomee
|
|
Three-term recurrence relation
|
|
Tight sequence
|
|
Time dependent elliptic problem
|
|
Time dependent elliptic variational problem
|
|
Time discretization of penalty term section
|
|
Time series forecasting section
|
|
Time-weak backward Kolmogorov
|
|
Time-weak problem
|
|
Total_probability_rule
|
|
Toy approximation in energy norm
|
|
Toy problem
|
|
Trace theorem
|
|
Trace-zero functions in W1p
|
|
Tranche_loss
|
|
Transformation of SDE based on delta hedging section
|
|
Transformation of SDE under change of measure
|
|
Transformation of parabolic problem 1
|
|
Transformation of parabolic problem 2
|
|
Transformation_to_heat_eq_section
|
|
Transition function
|
|
Transitive_bayes_formula
|
|
Transport of polynomial
|
|
Trigonometry primer
|
|
Two_asset_change_of_numeraire_section
|
|
Unbounded existence result
|
|
Uniform continuity of chf
|
|
Uniform convergence
|
|
Uniform property of vague convergence
|
|
Uniformly equicontinuous sequence
|
|
Uniformly smooth approximation lemma
|
|
Union property
|
|
Uniqueness of weak solution for the parabolic Dirichlet problem
|
|
Unscented conditions for mean
|
|
Unscented covariance summary
|
|
Unscented mean section
|
|
Unscented mean summary
|
|
Unscented transformation section
|
|
Unsuitability of spline wavelets
|
|
Unsuitability of spline wavelets 2
|
|
Upscaling
|
|
Useful formula
|
|
V for linear MRA 0
|
|
V for linear MRA d
|
|
V0 for linear MRA
|
|
Vague convergence
|
|
Vague convergence as a weak convergence 1
|
|
Vague convergence as a weak convergence 2
|
|
Vague convergence section
|
|
Vague precompactness of spm
|
|
Vanishing moments for biorthogonal wavelets section
|
|
Vanishing moments of wavelet section
|
|
Vanishing moments vs approximation
|
|
Vanishing moments vs approximation 2
|
|
Vanishing moments vs approximation 3
|
|
Vanishing moments vs decay at infinity
|
|
Variance of target process
|
|
Variance swap pricing section
|
|
Variational Dirichlet problem for generic parabolic operator
|
|
Variational inequalities chapter
|
|
Variational inequalities in maximization case
|
|
Variational inequality example
|
|
Variational toy problem
|
|
Visualization lemma
|
|
Vladimirov
|
|
W1p embedding
|
|
Walnut
|
|
Wavelet analysis section
|
|
Wavelet approximation 1
|
|
Wavelet approximation 2
|
|
Wavelet approximation 3
|
|
Wavelet approximation 4
|
|
Wavelet calculations chapter
|
|
Wavelet estimates in Sobolev spaces section
|
|
Wavelets on 01 step 1
|
|
Weak backward Kolmogorov with respect to time
|
|
Weak compactness of bounded set
|
|
Weak derivative
|
|
Weak derivative section
|
|
Weak duality theorem
|
|
Weak formulation of stationary problem
|
|
Weak formulation with respect to time parameter
|
|
Weak formulation with respect to time parameter section
|
|
Weak maximal principle 1
|
|
Weak solution of elliptic Dirichlet problem
|
|
Weak solution of parabolic Dirichlet problem
|
|
Weierstrass theorem
|
|
Whittaker sampling theorem
|
|
Why_Ito_process_section
|
|
Wiener-Hopf technique
|
|
Wilmott123
|
|
X to Y connection
|
|
XY_bracket
|
|
Xu
|
|
Yang
|
|
Young inequality
|
|
Zeros of orthogonal polynomials
|
|
Zorn maximal principle
|
|
[0,1]-adapted GMRAs
|
|
[0,1]-adapted MRA
|
|
definition of minmax p
|
|
ess sup definition
|
|
generalized impulse equation
|
|
generalized impulse solution
|
|
l2
|
|
log contract section
|
|
martingaleX
|
|
operations on sets section
|
|
q_mu_1
|
|
recovery of implied distribution
|
|
static replication formula
|
|
step function
|