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

Vlad Bally 1 Bruno Saussereau
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
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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https://hal.inria.fr/inria-00071781
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 6:46:12 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:07 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:37:42 PM

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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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