Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs. (Comparison of Lyapunov exponents of multiplicative Markov processes)
type: Item
instance of: scholarly article
title: Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs. (Comparison of Lyapunov exponents of multiplicative Markov processes)
zbMATH Open document ID: 0672.60034
author: Philippe Bougerol
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77335
review text: The author deals with conditions ensuring that the Lyapunov exponents of a cocycle of random matrices over a Markov chain are distinct. He treats linear Ito equations with Markovian coefficients and cocycles of diffeomorphisms derived from nonlinear stochastic differential equations as particular cases. He proves that the Lyapunov spectrum of the gradient Brownian motion on a compact hypersurface V in \({\mathbb{R}}^{d+1}\) is simple except V is a sphere (of radius r) in which case all exponents are equal to \(-d/2r^ 2\).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J57
Mathematics Subject Classification ID: 60K15
zbMATH DE Number: 4100291
zbMATH Keywords: products of random matrices
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: cocycle of random matrices
zbMATH Keywords: Lyapunov spectrum
reviewed by: Ludwig Arnold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4100291