A note on regularity property of stochastic convolutions for a class of functional differential equations

Abstract

Abstract This is a continuation of [5] which is concerned about the regularity property of stochastic convolutions for abstract linear stochastic retarded differential equations with unbounded operators on delay terms. In this work, we improve and generalize the main results in [5] by considering those delay operators which may have the same order as the infinitesimal generator of the system under consideration. To this end, we need restrict the weight function of distributed delay term to be Hölder continuous type in this system.