Strong Unique Continuation Property for Stochastic Parabolic Equations

TL;DR

This paper proves a strong unique continuation property for stochastic parabolic equations using a novel stochastic Carleman estimate, marking the first such result in stochastic PDEs.

Contribution

It introduces the first strong unique continuation result for stochastic PDEs, employing a new stochastic Carleman estimate method.

Findings

Established strong unique continuation for stochastic parabolic equations.

Developed a stochastic Carleman estimate technique.

First known result of its kind in stochastic PDE literature.

Abstract

We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation property of stochastic partial differential equations.