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arXiv · 1107.5774

Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems

Qi Lu
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Abstract

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic heat process through the observation at the final time $T$, for which we obtain a conditional stability estimate. The other is an inverse source problem with observation on the lateral boundary. We derive the uniqueness of the source.

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Qi Lu. 2011-07-28. Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems. https://doi.org/10.1088/0266-5611%2F28%2F4%2F045008

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