Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 67-91

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

Received 4 August 2003

Copyright © 2004 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.


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.