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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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https://tel.archives-ouvertes.fr/tel-00524212
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Submitted on : Tuesday, October 12, 2010 - 12:09:54 PM
Last modification on : Thursday, October 7, 2021 - 3:37:10 AM
Long-term archiving on: : Thursday, October 25, 2012 - 4:55:09 PM

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

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