Exponential asymptotic stability of linear Itô-Volterra equations with damped stochastic per\-tur\-bations (Q1767511)

This paper investigates the solutions of a \(d\)-dimensional linear stochastic integro-differential equation of the form \[ dX(t)= \Biggl(AX(t)+ \int^t_0 K(t- s)X(s)\,ds\Biggr)\,dt+ \Sigma(t) dW(t), \] where \(W\) is an \(r\)-dimensional Brownian motion with independent components. Theorems are proved concerning conditions leading to the exponential convergence of these solutions and concerning the implications of such convergence.