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Comportement asymptotique des processus de Markov auto-similaires positifs et forêts de Lévy stables conditionnées.

Abstract : Self-similar Markov processes often arise in various part of probability theory as limits of rescaled processes. TheMarkov property added to self-similarity provides some interesting features, as noted by Lamperti. The aim of the first part of this thesis is to describe the lower and the upper envelope through integral tests and laws of the iterated logarithm of a large class of positive self-similar Markov processes, as their future infimum and the positive slef-similar Markov process reflected at its future infimum. The second part deals with Lévy forest of a given size and conditioned by its mass. In paricular, an invariance principle for this conditioned forest is proved by considering a finite number of independent Galton-Watson trees whose offspring distribution is in the dommain of attraction of any stable law conditioned on their total progeny.
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https://tel.archives-ouvertes.fr/tel-00162262
Contributor : Juan Carlos Pardo Millan <>
Submitted on : Thursday, July 12, 2007 - 8:19:17 PM
Last modification on : Wednesday, December 9, 2020 - 3:12:27 PM
Long-term archiving on: : Monday, September 24, 2012 - 11:06:38 AM

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  • HAL Id : tel-00162262, version 1

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Juan Carlos Pardo Millan. Comportement asymptotique des processus de Markov auto-similaires positifs et forêts de Lévy stables conditionnées.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00162262⟩

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