TITLE: Stochastic Analogue of Stokes Theorem
QUESTION [6 upvotes]: Dynkin's formula can be thought of as the stochastic version of the Fundamental Theorem of calculus,
$$E^x[f(X_{\tau})]=f(x)+E^x\left[\int_0^{\tau}Af(X_u)du\right],$$
where $\tau$ is a first exit time and $A$ is the generator of the process $X_t$.
I'm wondering what the stochastic version of the Stokes theorem, say on a surface with boundary, should be?

REPLY [4 votes]: See, e.g., "Integral of differential forms along the path of diffusion processes" by Ikeda and Manabe. Perhaps the "Stokes theorem" in Malliavin's book is also of interest.