Stochastic variational inequalities for elasto-plastic oscillators
type: Item
instance of: scholarly article
title: Stochastic variational inequalities for elasto-plastic oscillators
zbMATH Open document ID: 1111.60050
author: Alain Bensoussan
author: Janos Turi
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2006-12-14T00:00:00Z
review text: The authors investigate a nonlinear oscillator equation of the form \[ \ddot{x}+c_0\dot{x}+F[x(0,t)]=\dot{w},\qquad x(0)=z,\;\dot{x}(0)=y, \] where \(F[x(0,t)]\) is a nonlinear functional depending on the path between \(0\) and \(t\), and \(\dot w\) is a white noise. It is shown that the pair \(\dot x\), \(F[x(0,t)]\) is the unique solution of the stochastic variational inequality \[ \dot{y}+c_0y+kz=\dot{w},\quad (\dot{z}-y)(\zeta-z)\geq 0 \text{ for}\;| \zeta| \leq Y, | z(t)| \leq Y, \] with \(y(0)=y\), \(z(0)=z\) (putting \(y(t)=\dot{x}(t)\), \(kz(t)=F[x(0,t)]\)). The process \((z,y)\) is Markov and its invariant measure is characterized by a partially degenerate elliptic partial differential equation with some Dirichlet coupling conditions.
reviewed by: Tomasz Bojdecki
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 5080178
zbMATH Keywords: Nonlinear oscillator excited by white noise
zbMATH Keywords: variational inequality
zbMATH Keywords: invariant measure
MaRDI profile type: Publication
full work available at URL: j.crma.2006.08.008
OpenAlex ID: W2060539876
cites work: Q5822308
cites work: Stability of regime-switching stochastic differential equations
cites work: Random vibration and spectral analysis
cites work: Q3995330
DOI: 10.1016/J.CRMA.2006.08.008
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description: scientific article; zbMATH DE number 5080178