Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 89729, 29 pages

Stabilization of Volterra equations by noise

John A. D. Appleby and Aoife Flynn

School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

Received 22 December 2004; Revised 10 March 2005; Accepted 11 March 2005

Copyright © 2006 John A. D. Appleby and Aoife Flynn. 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 paper studies the stability of an autonomous convolution Itô-Volterra equation where the linear diffusion term depends on the current value of the state only, and the memory of the past fades exponentially fast. It is shown that the presence of noise can stabilize an equilibrium solution which is unstable in the absence of this noise.