Journal of Applied Mathematics and Stochastic Analysis 
Volume 2008 (2008), Article ID 473156, 27 pages
doi:10.1155/2008/473156
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

Recommended by Jiongmin Yong

Abstract

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.