On symmetric fuzzy stochastic Volterra integral equations with retardation

TL;DR

This paper investigates symmetric fuzzy stochastic Volterra integral equations with retardation, establishing existence, uniqueness, and continuous dependence of solutions under Lipschitz and continuity conditions.

Contribution

It introduces a well-posedness framework for symmetric fuzzy stochastic Volterra equations with retardation, a novel aspect in the study of fuzzy stochastic integral equations.

Findings

Existence and uniqueness of solutions are proven.

Solutions depend continuously on initial parameters.

Conditions include Lipschitz continuity and kernel continuity.

Abstract

This paper contains a study on stochastic Volterra integral equations with fuzzy sets-values and involving on a constant retardation. Moreover, the form of the equation is symmetric in the sense that fuzzy stochastic integrals are placed on both sides of the equation. We show that the considered initial value problem formulated in terms of symmetric fuzzy stochastic Volterra integral equation is well-posed. In particular, we show that there exists a unique solution and this solution depends continuously on the parameters of the equation. The results are achieved with the conditions of Lipschitz continuity of drift and diffusion coefficients, and continuity of kernels