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

Da Prato, Giuseppe; Lunardi, Alessandra; Tubaro, Luciano

doi:10.1090/tran/7195

Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces
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by Giuseppe Da Prato, Alessandra Lunardi and Luciano Tubaro PDF

Trans. Amer. Math. Soc. 370 (2018), 5795-5842 Request permission

Abstract:

We construct surface measures in a Hilbert space endowed with a probability measure $\nu$. 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 $\nu$ 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.

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