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

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.