3.2 Problems and Solutions
3.2.1 Itō Calculus
- 1. Itō Integral. Let
be a probability space and let
be a standard Wiener process. Let the Itō integral of
be defined as the following limit
where
,
for
.
Show that the quadratic variation of
is
and hence
Finally, show that the Itō integral is a martingale.
Solution
For the first part of the solution, see Problem 2.2.6.1 (page 89).
Given
and ...
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