Open Access

Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity

Advances in Difference Equations20072007:065012

https://doi.org/10.1155/2007/65012

Received: 25 December 2006

Accepted: 8 May 2007

Published: 12 June 2007

Abstract

Stochastic difference second-kind Volterra equation with continuous time and small nonlinearity is considered. Via the general method of Lyapunov functionals construction, sufficient conditions for uniform mean square summability of solution of the considered equation are obtained.

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Authors’ Affiliations

(1)
Dipartimento di Matematica e Informatica, Universita di Salerno
(2)
Department of Higher Mathematics, Donetsk State University of Management

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Copyright

© B. Paternoster and L. Shaikhet. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.