Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces
type: Item
instance of: scholarly article
title: Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces
zbMATH Open document ID: 1154.60053
author: Kai Liu
published in: Statistics \& Probability Letters
publication date: 2008-09-29T00:00:00Z
review text: The author studies a class of retarded Langevin equations in a separable Hilbert space. He characterizes the existence of an invariant stationary mild solution by means of the covariance operator, Green's operator and the mean square boundedness for the solution starting in zero. Additionally he gives a sufficient existence criterion by the corresponding Lyapunov equation. The covariance operator of a stationary mild solution solution can be described as the solution of some retarded operator equation.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 5348285
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: Gaussian processes
zbMATH Keywords: stationary mild solutions
zbMATH Keywords: Lyapunov equation
reviewed by: Michael Högele
MaRDI profile type: Publication
full work available at URL: j.spl.2008.01.026
OpenAlex ID: W2055720681
cites work: On processes of ornstein-uhlenbeck type in hilbert space
cites work: Stochastic Equations in Infinite Dimensions
cites work: Ergodicity for Infinite Dimensional Systems
cites work: Langevins stochastic differential equation extended by a time-delayed term
cites work: Stability of functional partial differential equations
cites work: Stochastic Retarded Evolution Equations: Green Operators, Convolutions, and Solutions
cites work: Optimal control of linear retarded systems in Banach spaces
cites work: Structural properties of functional differential equations in Banach spaces
cites work: Theory and applications of partial functional differential equations
DOI: 10.1016/J.SPL.2008.01.026
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description: scientific article; zbMATH DE number 5348285