Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 67-91
doi:10.1155/S1687183904308022

Lyapunov functionals construction for stochastic difference second-kind Volterra equations with continuous time

Leonid Shaikhet

Department of Mathematics, Informatics, and Computing, Donetsk State Academy of Management, 163a Chelyuskintsev street, Donetsk 83015, Ukraine

Abstract

The general method of Lyapunov functionals construction which was developed during the last decade for stability investigation of stochastic differential equations with aftereffect and stochastic difference equations is considered. It is shown that after some modification of the basic Lyapunov-type theorem, this method can be successfully used also for stochastic difference Volterra equations with continuous time usable in mathematical models. The theoretical results are illustrated by numerical calculations.