Unique continuation for stochastic heat equations

Abstract

In this paper, we establish a unique continuation property for stochastic heat equations evolved in a convex domain G ⊂ R n (n ∈ N) with homogeneous Dirichlet boundary condition, which shows that the value of the solution can be determined by means of the observation on arbitrary open domain of G at arbitrary given time. Further, if G is bounded, we obtain a quantitative version of the unique continuation property.