Advances in Difference Equations
Volume 2008 (2008), Article ID 932831, 22 pages
doi:10.1155/2008/932831

Asymptotic representation of the solutions of linear Volterra difference equations

Abstract

This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which are given by a limit formula. This result is then used to obtain the exact asymptotic representation of the solutions of a class of convolution scalar difference equations, which have real characteristic roots. We give examples showing the accuracy of our results.