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Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion

Journal of Theoretical Probability volume 35, pages 410–425 (2022)Cite this article

Abstract

In this paper, we build the Wong–Zakai approximation for Stratonovich-type stochastic differential equations driven by G-Brownian motion and obtain the quasi-sure convergence rate under Hölder norm by a rough path argument. As a corollary, we obtain the quasi-continuity of solutions of random rough differential equations driven by lifted martingales under a sequence of singular measures.

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Acknowledgements

H.Z. is supported by the Youth Program of National Natural Science Foundation No. 11901104 and Postdoctoral Science Foundation of China.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, China

    Shige Peng

  2. School of Mathematics, Fudan University, Shanghai, China

    Huilin Zhang

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  1. Shige Peng
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  2. Huilin Zhang
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Correspondence to Huilin Zhang.

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Peng, S., Zhang, H. Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion . J Theor Probab 35, 410–425 (2022). https://doi.org/10.1007/s10959-020-01058-1

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  • DOI: https://doi.org/10.1007/s10959-020-01058-1

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