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Grandes déviations autonormalisées pour des chaînes de Markov

Abstract : The main objective of this thesis is to state self-normalized large deviations principles, mainly for Markovian models. Self-normalization allows a weakening of the assumptions made to obtain large deviations principles (as an example, for empirical means of a random variables sequence ). The key is the statement of a partial large deviations principle for some couples of random variables. The method to achieve this is to obtain a weak large deviation principle and an exponential tightness property for the couple. Contraction technics are also developped to deduce a weak LDP for $\left( \int f dL_n\right)$ from a weak LDP for sequences of empirical probability measures $(L_n)_n$. In particular, we prove self-normalized results in the Markovian framework, which generalize Dembo and Shao's work in the i.i.d. case.
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Contributor : Mathieu Faure <>
Submitted on : Wednesday, March 2, 2011 - 12:21:57 PM
Last modification on : Wednesday, November 28, 2018 - 2:48:22 PM
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  • HAL Id : tel-00572835, version 1



Mathieu Faure. Grandes déviations autonormalisées pour des chaînes de Markov. Mathématiques [math]. Université de Marne la Vallée, 2002. Français. ⟨tel-00572835⟩



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