Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs

TL;DR

This paper establishes uniqueness in law for certain parabolic SPDEs driven by space-time white noise, using an approach based on infinite-dimensional SDE systems, with the functional A(u) being Hölder continuous of order > 1/2.

Contribution

It introduces a novel method linking parabolic SPDEs to infinite-dimensional SDE systems to prove uniqueness in law under specific regularity conditions.

Findings

Proves uniqueness in law for a class of parabolic SPDEs.

Develops a new approach connecting SPDEs and infinite-dimensional SDEs.

Handles functionals A(u) with Hölder continuity of order greater than 1/2.

Abstract

We prove uniqueness in law for a class of parabolic stochastic partial differential equations in an interval driven by a functional A(u) of the temperature u times a space-time white noise. The functional A(u) is H\"older continuous in u of order greater than 1/2. Our method involves looking at an associated system of infinite-dimensional stochastic differential equations and we obtain a uniqueness result for such systems.