Support theorem for an SPDE with multiplicative noise driven by a cylindrical Wiener process on the real line

TL;DR

This paper establishes a support theorem for a class of SPDEs on the real line driven by cylindrical Wiener noise, extending support results to infinite-dimensional stochastic systems.

Contribution

It proves a support theorem for SPDEs with cylindrical Wiener noise on the real line, combining Mackevicius's diffusion approach and Krylov's $L_p$-theory.

Findings

Support theorem for SPDEs with cylindrical Wiener noise

Extension of support results to infinite-dimensional systems

Method combines diffusion approach with $L_p$-theory

Abstract

We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation (SPDE) on the real line with a noise term driven by a cylindrical Wiener process on $L_2 (\mathbb{R})$. The main ingredients of the proof are V. Mackevicius's approach to support theorem for diffusion processes and N.V. Krylov's $L_p$-theory of SPDEs.