INTERPRETATIONS PROBABILISTES D'OPERATEURS SOUS FORME DIVERGENCE ET ANALYSE DE METHODES NUMERIQUES ASSOCIEES

Miguel Martinez 1
1 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : The analysis and approximation of soutions of Stochastic Differential Equations (S.D.E.) having discontinuous coefficients is a subject that has not yet been given a satisfactory treatment. This problem becomes particulary motivating when solutions of certain Partial Differential Equations (P.D.E.) that also involve discontinuous coefficients, are beeing approximated using Monte-Carlo methods. This is for example the case, well-known in Physics, of P.D.Es involving a Divergence Form Operator (D.F.O.) with discontinuous coefficients : discontinuities are then closely related to the media where evolves the system under study. This thesis gives new results for the analysis and approximation of solutions of S.D.Es that are related to a D.F.O. with discontinuous coefficients. Statistical aspects of the models in play are also studied.
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Theses
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Submitted on : Thursday, July 15, 2004 - 5:00:24 PM
Last modification on : Monday, April 16, 2018 - 10:41:34 AM
Long-term archiving on: Wednesday, September 12, 2012 - 4:40:17 PM

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Miguel Martinez. INTERPRETATIONS PROBABILISTES D'OPERATEURS SOUS FORME DIVERGENCE ET ANALYSE DE METHODES NUMERIQUES ASSOCIEES. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2004. Français. ⟨tel-00006472⟩

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