Method of stochastic normal forms
type: Item
instance of: scholarly article
title: Method of stochastic normal forms
zbMATH Open document ID: 0762.58025
DOI: 10.1016/0020-7462(91)90042-R
author: S. Singh
published in: International Journal of Non-Linear Mechanics
publication date: 1993-01-16T00:00:00Z
review text: The paper presents calculations of normal forms for stochastic differential equations in \(\mathbb{R}^ n\) of the form \(\dot x=A(\eta)x+f(x,\eta)+\sigma F(x,\xi(t),\eta)\), where \(A\) is an \(n\times n\)-matrix, \(\xi\) is a stationary mean zero process, \(\eta\) and \(\sigma\) apparently are real paramters, \(f\) and \(A\) are smooth, \(f(0,\eta)\equiv F(0,\xi(t),\eta)\equiv 0\), and for \(\sigma=0\) the system is assumed to undergo a codimension one bifurcation in the parameter \(\eta\) at \(\eta=0\). It seems that further assumptions, in particular on the nature of \(\xi\), are made implicitly later.
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 92817
zbMATH Keywords: normal forms
zbMATH Keywords: stochastic differential equations in \(\mathbb{R}^ n\)
reviewed by: Hans Crauel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 92817