Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 473156, 27 pages
Research Article

Characterisation of Exponential Convergence to Nonequilibrium Limits for Stochastic Volterra Equations

John A. D. Appleby,1 Siobhán Devin,2 and David W. Reynolds1

1School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
2School of Mathematical Sciences, University College Cork, Cork, Ireland

Received 25 October 2007; Accepted 11 May 2008

Academic Editor: Jiongmin Yong

Copyright © 2008 John A. D. Appleby et al. 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.


This paper considers necessary and sufficient conditions for the solution of a stochastically and deterministically perturbed Volterra equation to converge exponentially to a nonequilibrium and nontrivial limit. Convergence in an almost sure and pth mean sense is obtained.