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Brownian Motion, 2nd Edition by Björn Böttcher, Lothar Partzsch, René L. Schilling

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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.

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

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with a partition Π = {0 = to < t1 < ... < tN = T} and θl = tl-1 + α(tl - tl-1) for some α ∈ [0,1]. This means that the character ...

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