Application of the general method of Lyapunov functionals construction for difference Volterra equations
type: Item
instance of: scholarly article
title: Application of the general method of Lyapunov functionals construction for difference Volterra equations
zbMATH Open document ID: 1069.39011
DOI: 10.1016/S0898-1221(04)90111-3
author: Leonid Shaikhet
author: Beatrice Paternoster
publication date: 2005-03-08T00:00:00Z
review text: The paper is concerned with a stochastic difference equation in the form \[ x_{i+1}=\eta_{i+1} +F(i,x_0,\dots, x_i). \] The mean square integrability and asymptotical stability of the solution are studied by using the formal procedure of Lyapunov functionals. This procedure is demonstrated for a linear Volterra equation with constant coefficients. The region of mean square integrability is discussed for a special class of equations.
reviewed by: Rong Yuan
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 2142376
zbMATH Keywords: Lyapunov functionals
zbMATH Keywords: asymptotic stability
zbMATH Keywords: stochastic difference equation
zbMATH Keywords: mean square integrability
zbMATH Keywords: linear Volterra equation
MaRDI profile type: Publication
cites work: Stability of functional differential equations
cites work: Q4209312
cites work: Riccati equations in the stability of retarded stochastic linear systems
cites work: Q4317058
cites work: Q4868382
cites work: Q3127183
cites work: Q4845419
cites work: Q4396394
cites work: Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations
cites work: Q4454229
cites work: Q4949216
cites work: A method for constructing Lyapunov functionals
cites work: About stability of nonlinear stochastic difference equations
cites work: Stabilization of inverted pendulum by control with delay.
cites work: Some peculiarities of the general method of Lyapunov functionals construction
published in: Computers & Mathematics with Applications
Recommended article: Q3633071
Recommended article: Q4513275
Recommended article: Difference equations of Volterra type and extension of Lyapunov's method
Recommended article: Lyapunov functionals construction for stochastic difference second-kind Volterra equations with continuous time
Recommended article: Q4868382
Recommended article: On the application of the Lyapunov second method to the Volterra difference equations
Recommended article: On the Lyapunov functionals method in the stability problem of Volterra integro-differential equations
Recommended article: Generalized Lyapunov approach for functional differential inclusions
Recommended article: GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME
Recommended article: About one application of the general method of Lyapunov functionals construction
description: scientific article; zbMATH DE number 2142376