Global solution to non-self-adjoint stochastic Volterra equation

AuthorsMojtaba Kiyanpour, Bijan Z. Zangeneh, Ruhollah Jahanipur
JournalStochastics and Dynamics
Paper TypeFull Paper
Published At2022-7-26
Journal GradeISI
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of

Abstract

In this paper, we establish the existence and uniqueness of the mild solution for stochastic Volterra equation with a non-self-adjoint operator.The specific Volterra equation that we consider is a generalization of the fractional differential equation. To obtain the mild solution for the case of multiplicative problem, the resolvent property of the linear perturbation of a sectorial operator will be considered.