Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces

Abstract

We construct surface measures in a Hilbert space endowed with a probability measure ν \nu . The theory fits for invariant measures of some stochastic partial differential equations such as Burgers and reaction–diffusion equations. Other examples are weighted Gaussian measures and special product measures ν \nu of non-Gaussian measures. In any case we prove integration by parts formulae on sublevel sets of good functions (including spheres and hyperplanes) that involve surface integrals.