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Equations aux dérivées partielles déterministes et stochastiques avec opérateurs fractionnaires

Abstract : This thesis treats application of fractional calculus in stochastic analysis. In the first part, the definition of the the multidimensional Riesz-Feller fractional differential operator is extended to higher order. The operator obtained generalizes several known fractional differential and pseudodifferential operators. High order fractional Fokker-Plank equations are studied in both the probabilistic and the quasiprobabilistic approaches. In particular, the solutions are represented via stable Lévy processes and generalization of Airy's function. In the second part, onedimensional stochastic fractional partial differential equations perturbed by space-time white noise are considered. The existence and the uniqueness of field solutions and of L2solutions are proved under different Lipschtz conditions. Spatial and temporal Hölder exponents of the field solutions are obtained. Further, equivalence between several definitions of L2solutions is proven. In particular, Fourier transform is used to give meaning to some stochastic fractional partial differential equations.
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Submitted on : Thursday, March 29, 2018 - 10:41:25 AM
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Latifa Debbi. Equations aux dérivées partielles déterministes et stochastiques avec opérateurs fractionnaires. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10046⟩. ⟨tel-01746621⟩



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