Stability and convergence via Lyapunov-like functionals of stochastic parabolic partial differential equations
type: Item
instance of: scholarly article
title: Stability and convergence via Lyapunov-like functionals of stochastic parabolic partial differential equations
zbMATH Open document ID: 1071.60052
author: Yanyan Li
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The authors consider Itô-type stochastic parabolic partial differential equations with a one-dimensional Wiener process as a driving process. A comparison theorem is established, employing vector Lyapunov-like functionals and ordinary differential equations, and further, a theorem is given which provides a construction of the comparison system. The authors present several notions of convergence of the solution process to zero, e.g., convergence in \(p\)th moment or convergence in probability of the \(p\)th moment, and of stability of the zero solution of the stochastic parabolic partial differential equation. Appropriate notions for the deterministic comparison system of ordinary differential equations are also given. Then results stating that a convergence or stability property of the deterministic system implies a corresponding property of the stochastic system are provided. The results are illustrated with an example.
reviewed by: Evelyn Buckwar
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 2117986
zbMATH Keywords: Wiener process
zbMATH Keywords: comparison theorem
zbMATH Keywords: Lyapunov-type functional
zbMATH Keywords: \(p\)th moment convergence
zbMATH Keywords: \(p\)th moment stability
MaRDI profile type: Publication
full work available at URL: j.amc.2003.08.032
OpenAlex ID: W2060511030
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DOI: 10.1016/J.AMC.2003.08.032
description: scientific article; zbMATH DE number 2117986