Abstract
We give the probabilistic interpretation of the solutions in Sobolev spaces of parabolic semilinear stochastic PDEs in terms of Backward Doubly Stochastic Differential Equations. This is a generalization of the Feynman–Kac formula. We also discuss linear stochastic PDEs in which the terminal value and the coefficients are distributions.
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Bally, V., Matoussi, A. Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations. Journal of Theoretical Probability 14, 125–164 (2001). https://doi.org/10.1023/A:1007825232513
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DOI: https://doi.org/10.1023/A:1007825232513