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Irregular Perturbations and Rough Differential Systems

Abstract : In this work we investigate a priori ill-posed differential systems from an analytic and probabilistic point of view. Thanks to technics inspired by the rough path theory and pathwise study of stochastic processes, we want to define those ill-posed systems and then study them. The first chapter of this thesis is related to ordinary differential equations perturbed by some irregular (stochastic) processes and the effects induced by the regularization of such processes. The second chapter deals with the linear transport equation multiplicatively perturbed by a rough path. Finally, in the last chapter we investigate the stochastic quantization equation Phi4 in three dimensions.
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Rémi Catellier. Irregular Perturbations and Rough Differential Systems. General Mathematics [math.GM]. Université Paris Dauphine - Paris IX, 2014. English. ⟨NNT : 2014PA090032⟩. ⟨tel-01121928⟩

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