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Unique continuation for stochastic parabolic equations. (English) Zbl 1224.60163
Summary: This paper is devoted to the study of the unique continuation property for stochastic parabolic equations. For solutions in the stochastic situation are adapted processes, classical approaches to treat the unique continuation problem for deterministic equations do not work. Here, the method is based on a suitable partial Holmgren coordinate transform and a stochastic version of the Carleman estimate.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35B60 Continuation and prolongation of solutions to PDEs
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