Advances in Difference Equations
Volume 2007 (2007), Article ID 65012, 13 pages
Research Article

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

Beatrice Paternoster1 and Leonid Shaikhet2

1Dipartimento di Matematica e Informatica, Universita di Salerno, Fisciano (Sa) 84084, Italy
2Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev 163-a, Donetsk 83015, Ukraine

Received 25 December 2006; Accepted 8 May 2007

Academic Editor: Roderick Melnik

Copyright © 2007 Beatrice Paternoster and Leonid Shaikhet. 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.


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.