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Statistiques d'extrêmes du mouvement brownien et applications

Abstract : This PhD thesis focuses on extreme-value problems in the context of Brownian motion, both in dimension 1 and 2. In dimension 1, we derive the joint probability distribution of the maximum and time at which the maximum is attained for n independent Brownian motions on a fixed time-interval. In dimension 2, making use of the 1-dimensional results, we derive the average values of the perimeter and area of the convex hull of n independent Brownian paths (open or closed). We also describe some applications of these theoretical results.
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Submitted on : Tuesday, October 12, 2010 - 12:09:54 PM
Last modification on : Sunday, June 26, 2022 - 11:52:21 AM
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  • HAL Id : tel-00524212, version 1



Julien Randon-Furling. Statistiques d'extrêmes du mouvement brownien et applications. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2009. Français. ⟨NNT : ⟩. ⟨tel-00524212⟩



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