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Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators

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Abstract

We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by G-Brownian motion (G-BSDEs) with diagonal generators. Two methods, including the penalization method and the Picard iteration argument, are provided to prove the existence and uniqueness of the solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.

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Acknowledgements

The authors would like to thank Professor Peng Luo for helpful discussions. The authors also thank the editor and the referee for useful suggestions that improved the first version of the paper. Li’s work was supported by the Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program (Overseas) (No. 2023HWYQ-049), the National Natural Science Foundation of China (No. 12301178) and the Qilu Young Scholars Program of Shandong University. Liu’s work was supported by National Natural Science Foundation of China (No. 12201315) and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63221036).

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Authors and Affiliations

  1. Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, 266237, China

    Hanwu Li

  2. Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao, 266237, China

    Hanwu Li

  3. School of Mathematical Sciences, Nankai University, Tianjin, 300071, China

    Guomin Liu

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  1. Hanwu Li
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  2. Guomin Liu
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Contributions

All authors wrote the main manuscript text; in particular, Li presented the penalization method part and Liu presented the Picard iteration method part. All authors read and approved the final version of the manuscript.

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Correspondence to Guomin Liu.

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Li, H., Liu, G. Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators. J Theor Probab (2024). https://doi.org/10.1007/s10959-024-01334-4

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