Change of measure-based verification of Girsanov's
theorem statement.
e would like to calculate
the
described in the section (
Girsanov's
theorem
). The process
is given by the
SDE
in "the original measure" (see the section
(
Change of measure recipe)
).
The
should look like a standard Brownian motion under a new measure given by the
formula (
Definition of change of
measure
) with
.
We restate the result (
Change of
Brownian
motion
):
Hence the drift
is, in fact, the volatility of
:
We integrate for
and
conclude
Note the correct normalization
and the
property
