Advances in Difference Equations
Volume 2007 (2007), Article ID 65012, 13 pages
doi:10.1155/2007/65012
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
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.