Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 89729, 29 pages
Stabilization of Volterra equations by noise
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.