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

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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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

Keywords

  • G-expectation
  • rough paths
  • Wong–Zakai approximation
  • quasi-sure continuity

Mathematics Subject Classification (2020)

  • 60H10
  • 60H35
  • 34F05