Etude de systèmes différentiels fractionnaires

Abstract : This PhD thesis work is devoted to the study of some finite and infinite-dimensional differential systems driven by Hölder processes. The general strategy consists in adapting the rough paths methods, originally designed to handle standard systems only. More specifically, we consider the case of the Volterra systems, as well as the case of heat equations. This work also focuses on the spin-offs of the rough paths approach as far as stochastic systems are concerned, with a special attention to the fractional Brownian motion. Finally, a detailed analysis of several approximation schemes for the solutions is provided.
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Aurélien Deya. Etude de systèmes différentiels fractionnaires. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2010. Français. ⟨NNT : 2010NAN10070⟩. ⟨tel-01748651⟩

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