Stochastic Volterra equations in weighted spaces (Q973890)

The authors consider the asymptotic stability and decay rates (in various modes of convergence) of solutions to stochastically perturbed Volterra equations to the equilibrium solution of a related unperturbed deterministic Volterra equation. In particular it is shown that when the measure and state-independent diffusion coefficient of a linear Itô-Volterra equation lie in appropriate \(L^p\)-weighted spaces, the solution also lies in such a space in both a moment and an almost sure sense.