Unique Continuation for Stochastic Heat Equations

Abstract

We establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of $G$ at any given positive time constant. Further, when $G$ is convex and bounded, we also give a quantitative version of the unique continuation property. As applications, we get an observability estimate for stochastic heat equations, an approximate result and a null controllability result for a backward stochastic heat equation.

References in corpus (2)

• Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems
• Unique Continuation for Stochastic Parabolic Equations