Détection de la convergence de processus de Markov

Abstract : Our work deals with the cutoff phenomenon for n-samples of Markov processes, in order to apply it to the detection of convergence of parallelized algorithms. In a first part, the sampled process is an Ornstein-Uhlenbeck process. We point out the cutoff phenomenon for the n-sample, and we link it with the convergence in distribution of the hitting time of a fixed level by the average process. In a second part, the general case is studied, in which the sampled process is supposed to converge at exponential rate to its stationary distribution. Precise estimates are given for the distances between the distribution of the n-sample and its stationary distribution. Finally, we explain the way of dealing with some hitting time problems linked to the cutoff phenomenon.
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Submitted on : Friday, October 7, 2005 - 12:36:23 PM
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Béatrice Lachaud. Détection de la convergence de processus de Markov. Mathématiques [math]. Université René Descartes - Paris V, 2005. Français. ⟨tel-00010473⟩

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