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Exponential asymptotic stability of linear Itô-Volterra equations with damped stochastic perturbations. (English) Zbl 1065.60060
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.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34K20 Stability theory of functional-differential equations 34K50 Stochastic functional-differential equations 60H20 Stochastic integral equations 60H99 Stochastic analysis
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