- 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 limitwhere , 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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