Backward Doubly Stochastic Integral Equations of the Volterra Type

TL;DR

This paper investigates backward doubly stochastic Volterra integral equations, establishing conditions for their existence and uniqueness under Lipschitz assumptions, contributing to the mathematical understanding of such stochastic systems.

Contribution

It introduces the first comprehensive existence and uniqueness results for backward doubly stochastic Volterra integral equations under Lipschitz conditions.

Findings

Proved existence of solutions under Lipschitz assumptions

Established uniqueness of solutions for BDSIEVs

Provided a framework for analyzing stochastic Volterra equations

Abstract

In this paper, we study backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short). Under uniform Lipschitz assumptions, we establish an existence and uniqueness result.