Abstract
In this paper we investigate a class of semilinear stochastic Volterra equations which arise in the theory of heat conduction with memory effects, with dissipative nonlinearities and an additive stochastic term which models a rapidly varying external heat source. We first prove that the problem has a unique solution for all times; further, we analyze the asymptotic behavior of the solution and we prove the existence of an ergodic invariant measure.
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