Brownian Motion, 2nd Edition

20 Stratonovich’s stochastic calculus

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 < t₁ < ... < 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 ...