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Journal of Theoretical Probability

, Volume 14, Issue 1, pp 125–164 | Cite as

Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations

  • V. Bally
  • A. Matoussi
Article

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.

stochastic partial differential equation Backward Doubly SDE Feynman–Kac's formula stochastic flows Schwartz distributions weighted Sobolev spaces 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • V. Bally
    • 1
  • A. Matoussi
    • 2
  1. 1.Laboratoire de probabilités, Tour 56Université Paris VIParis Cedex 05France
  2. 2.Laboratoire Statistique et ProcessusUniversité du MaineLe Mans cedexFrance

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