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inria-00071781, version 1

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

Vlad Bally 1, Bruno Saussereau

N° RR-4805 (2003)

Résumé : 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.

  • 1 :  MATHFI (INRIA Rocquencourt)
  • INRIA – Ecole des Ponts ParisTech – Université Paris-Est Créteil Val-de-Marne (UPEC)
  • Domaine : Informatique/Autre
  • Mots-clés : BACKWARD DOUBLY SDES / MALLIAVIN CALCULUS / STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS / WEAK SOLUTIONS / WIENER CHAOS DECOMPOSITION
  • Référence interne : RR-4805
 
  • inria-00071781, version 1
  • http://hal.inria.fr/inria-00071781
  • oai:hal.inria.fr:inria-00071781
  • Contributeur : Rapport De Recherche Inria <>
  • Soumis le : Mardi 23 Mai 2006, 18:46:12
  • Dernière modification le : Mercredi 14 Mars 2007, 12:44:43