Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations

V. Bally and A. Matoussi
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V. Bally: Université Paris VI
A. Matoussi: Université du Maine

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 125-164

Abstract: 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.

Keywords: stochastic partial differential equation; Backward Doubly SDE; Feynman–Kac's formula; stochastic flows; Schwartz distributions; weighted Sobolev spaces (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (6)

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DOI: 10.1023/A:1007825232513

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