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Reports (Research Report) Year : 2003

A relative compactness criterion in Wiener-Sobolev spaces and application to semi-linear Stochastic P.D.Es

Vlad Bally
  • Function : Author
Bruno Saussereau
  • Function : Author

Abstract

We prove a relative compactness criterion in Wiener-Sobolev space which represents a natural extension of the compact embedding of sobolev space H^1 into L^2, at the level of random fields. Then we give a specific statement of this criterion for random fields solutions of semi-linear Stochastic Partial Differential Equations with coefficients bounded in an appropriate way. Finally, we employ this result to construct solutions for semi-linear Stochastic Partial Differential Equations with distribution as final condition. We also give a probabilistic interpretation of this solution in terms of Backward Doubly Stochastic Differential Equations formulated in a weak sense.
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Dates and versions

inria-00071781 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071781 , version 1

Cite

Vlad Bally, Bruno Saussereau. A relative compactness criterion in Wiener-Sobolev spaces and application to semi-linear Stochastic P.D.Es. [Research Report] RR-4805, INRIA. 2003. ⟨inria-00071781⟩
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