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Processus associés à l'équation de diffusion rapide. Indépendance du temps et de la position pour un processus stochastique

Abstract : The aim of this thesis is twofold. First, we give a stochastic modelisation of a partial differential equation known as equation of "fast" diffusion. The latter describes a diffusion phenomenon which occurs in the plasma physics. Thus, we study the solution of a differential stochastic equation, the density of which satisfies the equation of "fast" diffusion : we treat in particular the case when the initial measure is the Dirac measure at 0. Secondly, we deal with the question of the independence of time and position for a stochastic process. We consider a random walk S(n) with independent identically distributed increments and we study the standard stopping times T such that T and S(T) are independent. We give a description of the stopping distributions of S(T) in the case of a Bernoulli symmetric random walk. We finally complete this work by giving a characterization of the stopping distributions of the Brownian motion.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_2003_0186_ACKERMANN.pdf
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https://hal.univ-lorraine.fr/tel-01746825
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Submitted on : Thursday, March 29, 2018 - 10:45:34 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM

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Christophe Ackermann. Processus associés à l'équation de diffusion rapide. Indépendance du temps et de la position pour un processus stochastique. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10186⟩. ⟨tel-01746825⟩

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