Stochastic PDEs driven by G-Brownian motion and the associated Backward Doubly Stochastic Differential Equations

TL;DR

This paper investigates the existence, uniqueness, and relationships of quasilinear stochastic PDEs driven by G-Brownian motion and their associated backward doubly stochastic differential equations, expanding the theoretical framework of stochastic analysis.

Contribution

It establishes the well-posedness of G-Brownian driven SPDEs and links these equations to GBDSDEs, providing new insights into their analytical properties.

Findings

Proved existence and uniqueness of weak solutions for GSPDEs.

Solved the associated GBDSDEs.

Established the relation between GSPDEs and GBDSDEs.

Abstract

Our aim is to study the well-posedness of quasilinear stochastic partial differential equations driven by G-Brownian motion (GSPDEs for short) and the associated backward doubly stochastic differential equations (GBDSDEs for short). We first prove the existence and uniqueness of weak solution to GSPDEs by analytical approach, and then solve the corresponding GBDSDEs. Finally, the relation between GSPDEs and GBDSDEs is established.