Unique continuation for a fourth-order stochastic parabolic equation

Abstract

In this paper, we prove a boundary unique continuation property for a fourth-order stochastic parabolic equation evolving in a domain G⊂Rn. Our result shows that the value of the solution can be determined by the observation on an arbitrary open subset of the boundary. The quantitative version of this property can be derived by the global Carleman estimate, which is deduced from a weighted identity for a fourth-order stochastic parabolic operator. The results in this paper are also new even if the fourth-order stochastic parabolic equation reduces to the corresponding fourth-order deterministic parabolic equation.