# Taylor expansion to show that for Stratonovich stochastic calculus the chain rule takes the form of the classical one

As nobody seems to be able to give any kind of answer to that problem over there at math.stackexchange I post this question here:

How can I show with a heuristic argument based on a Taylor expansion that for Stratonovich stochastic calculus the chain rule takes the form of the classical (Newtonian) one?

The intuition goes like this: Concerning Ito calculus the fact that dX^2 = dt results via a Taylor expansion in Ito's lemma - this fact should stay the same with Stratonovich but it should somehow cancel out in there - I just don't know how...

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## 1 Answer

Hi,

Well you can have a look at the book of Kloeden and Platen "Numerical Solution of Stochastic Differential Equations" where the derivation of Taylor expansion for diffusion is derived based on iterated Wiener Itô (or Stratanovitch) Integrals.

Best Regards

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@The Bridge: Thank you for the reference. I have the book in front of me and had a cursory look at it... could you please provide me with the exact place where you found the reference for the above question - Thank you again! – vonjd Aug 11 '10 at 11:29
Well it is hard to answer this the derivation of Stratanovitch-Taylor expansion in this book is quite long. But in the end what you get is a classicla Taylor formula so it matches what was required in your question ins't it ? – The Bridge Aug 14 '10 at 16:12