%0 Journal Article
%T Unique Continuation for Stochastic Heat Equations
%A Qi Lu
%A Zhongqi Yin
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1305.3888v2