Itô’s integral does not obey the usual rules from classical deterministic differential calculus. This is sometimes disconcerting and a small variation in the definition of the stochastic integral can change this. We will, however, loose the property that the stochastic integral is a martingale.

A good starting point is Problem 15.15 (see also Example 15.15) where you have shown that

with a partition Π = {0 = t_{o} < t_{1} < ... < t_{N} = T} and θ_{l} = t_{l-1} + α(t_{l} - t_{l-1}) for some α ∈ [0,1]. This means that the character ...

Start Free Trial

No credit card required