Decomposition of stochastic flows and Lyapunov exponents
type: Item
instance of: scholarly article
title: Decomposition of stochastic flows and Lyapunov exponents
zbMATH Open document ID: 0970.58021
author: Ming Liao
publication date: 2001-02-18T00:00:00Z
review text: Consider a stochastic differential equation on a compact Riemannian manifold, and let \(\phi_t\) be the flow generated by this equation. For a fixed \(m\) in \(M\) and a fixed orthonormal frame \(u\) at \(m\), the author proves that this flow has a unique decomposition \(\phi_t=\xi_t\psi_t\), where \(\xi_t\) is an isometry, \(\psi_t(m)=m\), and the differential of \(\psi_t\) satisfies \(D\psi_t(u)=us_t\) for an upper triangular matrix \(s_t\). This decomposition can be applied to the study of the Lyapunov exponents \((\lambda_i)\) of the flow; the component \(\psi_t\) preserves the directions of tangent vectors at \(m\) corresponding to the rates \(\lambda_i\).
reviewed by: Jean Picard
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 37H15
zbMATH DE Number: 1525168
zbMATH Keywords: stochastic flows
zbMATH Keywords: Lyapunov exponents
MaRDI profile type: Publication
DOI: 10.1007/S004400000064
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1525168