Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Abstract

The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by G-Brownian motion (G-BSDEs). In fact, when the generators are Lipschitz continuous in y and uniformly continuous in z, we construct the unique solution to such equations by monotone convergence argument. The comparison theorem and related Feynman-Kac formula are stated as well.

Doubly Reflected Backward Stochastic Differential Equations Driven by G -Brownian Motion With a Kind of Non-Lipschitz Coefficients

“…and Zheng [35] studied G-BSDEs with uniformly continuous coefficients in z by a linearization method and a monotone convergence argument, Sun [34] extended the result to G-BSDEs with uniformly continuous coefficients in (y, z). Zhang and Jiang [37] studied G-BSDEs with a kind of non-lipschitz coefficients by the method of Picard iteration.…”