BV functions in Hilbert spaces

TL;DR

This paper explores functions of bounded variation in infinite-dimensional Hilbert spaces with probability measures, providing foundational characterizations and applying the theory to invariant measures of stochastic PDEs.

Contribution

It introduces a framework for BV functions in Hilbert spaces with differentiable measures and applies it to stochastic PDE invariant measures, advancing infinite-dimensional analysis.

Findings

Established basic characterizations of BV functions in Hilbert spaces.

Applied theory to invariant measures of stochastic PDEs.

Provided examples illustrating the theory's relevance.

Abstract

We study $BV$ functions in a Hilbert space $X$ endowed with a probability measure $\nu$, assuming that $\nu$ is Fomin differentiable along suitable directions. We establish basic characterizations, and we apply the general theory to relevant examples, including invariant measures of some stochastic PDEs.