Processus stochastiques associés aux équations d'évolution linéaires ou non-linéaires et méthodes numériques probabilistes

Madalina Deaconu 1, 2
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : The document contains results on the probabilistic approach of some linear and non-linear evolution equations and probabilistic numerical methods. The first part concerns some results on the connection between partial differential equations and stochastic processes for linear or non-linear models. An important part is devoted to the study of the probabilistic approach of coagulation and/or fragmentation models. We introduce in the second part new algorithms based on Monte-Carlo methods for a large class of stochastic differential equations. This method allows to simulate with high accuracy the first exit time and the exit position from a domain. We are interested also in importance sampling techniques in order to reduce the variance. In the third part we present results on the regularity of some stochastic processes in Besov spaces. And finally, in the fourth part, a brief presentation of some practical problems is done.
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Habilitation à diriger des recherches
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Madalina Deaconu. Processus stochastiques associés aux équations d'évolution linéaires ou non-linéaires et méthodes numériques probabilistes. Mathématiques [math]. Université Henri Poincaré - Nancy I, 2008. ⟨tel-00590778⟩

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