Construction of a surface integral under local Malliavin assumption and integration by parts formulae

Abstract

In this paper, we consider convex sets $K_r=\{g\ge r\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\mu$ in $H$. We first show how to define a surface measure on the level sets $\{g=r\}$ that is related to $\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories

22 pages

References in corpus (1)

• Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space

Cited by in corpus (2)

• Differentiability in infinite dimension and the Malliavin calculus
• Surface measures and integration by parts formula on levels sets induced by functionals of the Brownian motion in ${\mathbb{R}}^n$