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Processus stochastiques et équations aux dérivées partielles : applications des espaces de Besov aux processus stochastiques

Abstract : The first part of this thesis contains topics relating stochastic processes to partial differential equations via the stochastic differential equation. We prove first the convergence in law to the stationary distribution for a non-linear process, reflected in [-1, 1]. Two such stationary densities are computed and numerical results are presented. Further, we describe the behaviour of the hitting times for a strongly inward real diffusion. We consider next sorne reflected Brownian motions in the unit disk and we compute the maximum of the expectation of the time spent by this process in the disk. The second part of this work is devoted to sorne applications of Besov spaces to stochastic processes. We treat at the beginning the membership of the iterated Brownian motion to Besov and Besov-Orlicz spaces. We examine next the Besov regularity for a two indexed stochastic process, solution of the Walsh equation. The last application presents the approximation of a function in the d-dimensional cube by tensor product neural networks.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_1997_0064_DEACONU.pdf
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https://hal.univ-lorraine.fr/tel-01747413
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Submitted on : Thursday, March 29, 2018 - 10:59:17 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM

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Madalina Deaconu. Processus stochastiques et équations aux dérivées partielles : applications des espaces de Besov aux processus stochastiques. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1997. Français. ⟨NNT : 1997NAN10046⟩. ⟨tel-01747413⟩

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