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BSDEs driven by G-Brownian motion with time-varying uniformly continuous generators
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In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under the condition that the generator is time-varying Lipschitz continuous with respect to y and time-varying uniformly continuous with respect to z. With the help of linearization method and the G-stochastic analysis techniques, we construct the approximating sequences of G-BSDE and obtain some precise a priori estimates. By combining this with the approximation method, we prove the existence and uniqueness of the solution under the time-varying conditions, as well as the comparison theorem.
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Quadratic BSDEs with double constraints driven by G-Brownian motion
Claims well-posedness for quadratic G-BSDEs with double mean reflections, but the proof silently drops the f term and does not prove the stated f-inclusive theorem.
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