This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the unique continuation problem for deterministic equations do not work. Our method is based on a suitable partial Holmgren coordinate transform and a stochastic version of Carleman estimate.
"Unique continuation for stochastic parabolic equations." Differential Integral Equations 21 (1-2) 81 - 93, 2008.