Existence and uniqueness are proven for doubly reflected G-BSDEs with quadratic generators when the upper obstacle is nearly a generalized G-Itô process, along with a penalization approximation and PDE link.
and Peng, S.: Function spaces and capacity related to a sublinear expectation: application toG-Brownian motion pathes.Potential Anal.34, (2011), 139-161
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Doubly Reflected Backward SDEs Driven by $G$-Brownian Motion with Quadratic Generator
Existence and uniqueness are proven for doubly reflected G-BSDEs with quadratic generators when the upper obstacle is nearly a generalized G-Itô process, along with a penalization approximation and PDE link.