Skip to Main content Skip to Navigation
Theses

Contributions à l'étude d'une marche aléatoire centrifuge et théorèmes limites pour des processus aléatoires conditionnés.

Abstract : In the first part of this thesis, we study a model of centrifugal random walk. We prove a Law of Iterated Logarithm for its norm, and find the asymptotic law of the fluctuations of its direction. We then give upper and lower bounds for the exponential decay of the probability that the centrifugal random walk visits a fixed compact set at time n; this is achieved by proving that the probability that a centered random walk visits a compact set at time n without having left a cone does not decrease exponentially. In the second part, we study the multidimensional Brownian motion conditioned to stay in a circular cone for a unit of time, and derive an Invariance Principle for a random walk conditioned to stay in a circular cone.
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00366462
Contributor : Rodolphe Garbit <>
Submitted on : Saturday, March 7, 2009 - 3:39:34 PM
Last modification on : Thursday, March 5, 2020 - 5:32:50 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 9:23:46 PM

Identifiers

  • HAL Id : tel-00366462, version 1

Collections

Citation

Rodolphe Garbit. Contributions à l'étude d'une marche aléatoire centrifuge et théorèmes limites pour des processus aléatoires conditionnés.. Mathématiques [math]. Université François Rabelais - Tours, 2008. Français. ⟨tel-00366462⟩

Share

Metrics

Record views

480

Files downloads

646