Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 89729, 29 pages
doi:10.1155/JAMSA/2006/89729
Abstract
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.