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Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations |
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| Authors: | V. Bally A. Matoussi |
| Affiliation: | (1) Laboratoire de probabilités, Tour 56, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France;(2) Laboratoire Statistique et Processus, Université du Maine, BP 535, 72017 Le Mans cedex, France |
| 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 |
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