BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs

TL;DR

This paper establishes existence and uniqueness for G-BSDEs in degenerate cases and introduces a probabilistic approach to analyze the regularity of associated fully nonlinear PDEs.

Contribution

It provides the first existence and uniqueness results for G-BSDEs under degeneracy and links these to PDE regularity using a novel probabilistic method.

Findings

Proved existence and uniqueness of G-BSDEs in degenerate cases.

Developed a new probabilistic method for PDE regularity.

Connected G-BSDE solutions to the regularity of nonlinear PDEs.

Abstract

In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the representation theorem of G-expectation and weak convergence to obtain the regularity of fully nonlinear PDE associated to G-BSDE.