Closability of Quadratic Forms Associated to Invariant Probability Measures of SPDEs

TL;DR

This paper proves the closability of quadratic forms linked to invariant measures of certain SPDEs using Markov operator techniques, with applications to various infinite-dimensional stochastic systems.

Contribution

It introduces a general method for establishing the closability of quadratic forms associated with invariant measures of SPDEs, extending to systems with delay and Hamiltonian structures.

Findings

Proves closability of quadratic forms via Markov operator integration by parts.

Applies results to semilinear SPDEs and stochastic Hamiltonian systems.

Provides a framework for analyzing invariant measures in infinite dimensions.

Abstract

By using the integration by parts formula of a Markov operator, the closability of quadratic forms associated to the corresponding invariant probability measure is proved. The general result is applied to the study of semilinear SPDEs, infinite-dimensional stochastic Hamiltonian systems, and semilinear SPDEs with delay.