Strong solutions to stochastic Volterra equations

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Abstract

In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main results provide sufficient conditions for strong solutions to stochastic Volterra equations.

Keywords

Stochastic linear Volterra equation
Resolvent
Strong solution
Stochastic convolution

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Both authors are partially supported by Laboratorio de Análisis Estocástico, PBCT-ACT13.