Stochastic Analogue of Stokes Theorem

Question

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?

Answer 1

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.