Strong unique continuation property for stochastic parabolic equations

The unique continuation property has been extensively studied for partial differential equations. Nevertheless, this fundamental concept has not yet received sufficient investigation when it comes to stochastic partial differential equations. Particularly, to the best of our knowledge, there is no published work addressing the strong unique continuation property of stochastic partial differential equations. In this paper, we obtain a strong unique continuation property for stochastic parabolic equations. To achieve that, we establish a new stochastic version of the Carleman estimate.