A stochastic version of center manifold theory
type: Item
instance of: scholarly article
title: A stochastic version of center manifold theory
zbMATH Open document ID: 0671.58045
DOI: 10.1007/BF01845701
author: Petra Boxler
publication date: 1989-01-01T00:00:00Z
review text: Random dynamical systems arise naturally if the influence of white or real noise on the parameters of a nonlinear deterministic dynamical system is studied. In this situation Lyapunov exponents attached to the linearized flow replace the real parts of the eigenvalues and describe the stability behavior of the linear system. If at least one of them vanishes then it is possible to prove the existence of a stochastic analogue of the deterministic center manifold. The asymptotic behavior of the entire system can then be derived from the lower dimensional system restricted to this stochastic center manifold. A dynamical characterization of the stochastic center manifold is given and approximation results are proved.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 4098369
zbMATH Keywords: random dynamical systems
zbMATH Keywords: nonlinear deterministic dynamical system
zbMATH Keywords: real noise
zbMATH Keywords: eigenvalues
zbMATH Keywords: flow
zbMATH Keywords: stability
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4098369