Malliavin Calculus for non Gaussian differentiable measures and surface measures in Hilbert spaces

摘要

We construct surface measures in a Hilbert space endowed with a probabilitymeasure $\nu$. The theory fits for invariant measures of some stochasticpartial differential equations such as Burgers and reaction--diffusionequations. Other examples are weighted Gaussian measures and special productmeasures $\nu$ of non Gaussian measures; in this case we exhibit a Markovprocess having $\nu$ as invariant measure. In any case we prove integration byparts formulae on sublevel sets of good functions (including spheres andhyperplanes) that involve surface integrals.