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Théorèmes limites fonctionnels pour des U-statistiques échantillonnéees par une marche aléatoire. Étude de modèles stochastiques de repliement des protéines

Abstract : This work is divided into two separate parts. We first study the asymptotic behavior of $U$-statistics indexed by a random walk. Let $(S_(n))_(n\geq 0)$ be a $\Z^d-$random walk, with $d \geq 1$, and $(\xi_(x))_(x\in \\Z^d)$ be a sequence of independent and identically distributed $\R$-valued random variables, independent of the random walk. Let $h$ be a measurable, symmetric function defined on $\R^2$ with values in $\R$. We focus on the weak convergence of the sequence $\cU_(n), n\in \N$, with values in $D[0,1]$ the set of right continuous real-valued functions with left limits, defined by $$\sum_(i,j=0)^([nt])h(\xi_(S_(i)),\xi_(S_(j))), t\in[0,1].$$ \\ Cabus et Guillotin studied the case when, $(S_n)_(n \in \N)$, is $\Z^d$-valued, with $d \geq 2$. We solve the case when $d=1$ and we give a new proof of the results by Cabus and Guillotin.\\ In the second part, we consider different protein folding dynamics. We focus on the asymptotic behavior of their hitting time. For each dynamics, we prove a law of large number, a central limit theorem and we compare the performance of the models.
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https://tel.archives-ouvertes.fr/tel-00008740
Contributor : Veronique Ladret <>
Submitted on : Thursday, March 10, 2005 - 1:42:21 AM
Last modification on : Friday, June 3, 2016 - 1:04:23 AM
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Véronique Ladret. Théorèmes limites fonctionnels pour des U-statistiques échantillonnéees par une marche aléatoire. Étude de modèles stochastiques de repliement des protéines. Mathématiques [math]. Université Claude Bernard - Lyon I, 2004. Français. ⟨tel-00008740⟩

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