Hi,I was wondering if someone could help me out with this one:Compute integral(0,1)X(s)dX(s) as a Stratonovitch integral. Where X(s) is nonstandard Brownian motion. i.e. X(t)~N(0,t*sigma^2) Edit: Actually if anyone could explain how a Stratonovitch integral differs from an Ito integral that would also be very helpfulThanksJames

The Matlab Notebook has a good chapter on this type of problem. Are you having trouble getting started or have you hit a block?

Aaron thanks for the link, much appreciated.I will give it a read and if I am still stuck I will get back to you.ThanksJames

James, the excommunicated:there is one main difference, it doesn't look forward (sometimes it is called an anticipatory equation). Google away on this, search mid-point SDE, etc. There are some concrete and practical differences, though. Firstly, Stratonovich integals aren't martingales, but the can be transformed into Ito integrals. You can use the modified Ito equation to transform back and forth between interpretations. A standard example would be, let dW be a Stratonovich differential and let * be composition: dX = aXdt + bX*dW in the stratonocvich sense becomes dX = (a+b^2/2)Xdt + bXdw in the Ito. Also, you don't get second order term in the parts formula, which makes Stratonovich easier. So, in the end, it is mathematically more appealing, but it has some practical drawbacks, as well problems with interpretation. In applied areas people stick with Ito, whereas if you are studying Emory and SDE's on manifolds, Strat is better.Hope this helps

Chiral that did help. Thanks for tutoring the expelled pupil I appreciate it.Are stochastic integrals evaluated at the end point of the interval ever used? If so what is their practical relevance?James

Stratonovitch(-Fisk) integral has been used extensively in enginnering field, as well as stochastic calculus on manifold, if you use Ito, the representation of the system will depends on the local charts you use, but for Stratonovitch, you are fine...

M'gale, you sneaky little dude, what are you doing in the same thread as me here? This feels wierd, I need a shower.@James: Look around at the definitions of the two integrals and you will see what I mean regarding the points they are evaluated on. Also, that will explain how one is referred to as "anticipatory".

Thanks M'gale and Chiral.,Chiral I see what your saying as regards the points they are evaluated on.If we are integrating something of the form F(W)dW then,Ito would be:SUM [ F( W(i) )*( W(i+1) - W(i) ) ]Stratonovitch would be:SUM [ F( 0.5*(W(i+1) + W(i)) )*( W(i+1) - W(i) ) ]right?What about:SUM [ F( W(i+1) )*( W(i+1) - W(i) ) ]ie evaluated at the end point?