Symmetrical martingale solutions of backward doubly stochastic Volterra integral equations

TL;DR

This paper introduces symmetrical martingale solutions for backward doubly stochastic Volterra integral equations, establishing their existence and uniqueness, thus advancing the theoretical understanding of these complex stochastic integral equations.

Contribution

The paper defines SM-solutions for BDSVIEs and proves their existence and uniqueness, providing a new framework for analyzing these equations.

Findings

Established the existence of SM-solutions for BDSVIEs

Proved the uniqueness of SM-solutions for BDSVIEs

Provided a theoretical foundation for future research on BDSVIEs

Abstract

This paper aims to study a new class of integral equations called backward doubly stochastic Volterra integral equations (BDSVIEs, for short). The notion of symmetrical martingale solutions (SM-solutions, for short) is introduced for BDSVIEs. And the existence and uniqueness theorem for BDSVIEs in the sense of SM-solutions is established.