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Concentration et fluctuations de processus stochastiques avec sauts

Abstract : This PhD Thesis is divided into
two independent parts, the first one dealing with the
concentration of measure phenomenon for birth-death processes, whereas the second one is devoted to the analysis of the fluctuations of stochastic integrals driven by stable processes.
In the first part of the thesis, we explore the measure
concentration for birth-death processes. The various approaches considered are on the one hand the functional inequalities together with the Herbst method, and one the other hand the study
of the associated semigroup and martingales techniques. In particular, we are led to introduce some notions about curvatures of such processes, which are the discrete analogous of the
Bakry-Emery curvature criterion given for diffusion processes.
In the second part of the thesis, we study the behavior of the supremum process of a stable stochastic integral by providing maximal inequalities which are applied to passage time problems of
symmetric stable processes. Finally, we derive a convex domination principle for dependent Brownian and stable stochastic integrals.
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Contributor : Aldéric Joulin <>
Submitted on : Wednesday, November 22, 2006 - 5:39:08 PM
Last modification on : Friday, April 9, 2021 - 3:46:09 PM
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  • HAL Id : tel-00115724, version 1



Aldéric Joulin. Concentration et fluctuations de processus stochastiques avec sauts. Mathématiques [math]. Université de La Rochelle, 2006. Français. ⟨tel-00115724⟩



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