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arXiv · 2409.16574

BSDEs driven by G-Brownian motion with time-varying uniformly continuous generators

Bingru Zhao
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Abstract

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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Bingru Zhao. 2024-09-25. BSDEs driven by G-Brownian motion with time-varying uniformly continuous generators. https://arxiv.org/abs/2409.16574

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