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Stochastic Differential Equations with Perturbations Driven by G-Brownian Motion

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Abstract

In this study, we investigate asymptotic property of the solutions for a class of perturbed stochastic differential equations driven by G-Brownian motion (G-SDEs, in short) by proposing a perturbed G-SDE with small perturbation for the unperturbed G-SDE. We consider the closeness in the 2m-order moments of the solutions of perturbed G-SDEs and the unperturbed G-SDEs. At last, the obtained results are illustrated via a concrete example.

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Acknowledgements

The authors are deeply grateful to the editor and anonymous referees for the careful reading, valuable comments and correcting some errors, which have greatly improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Yong Ren

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641 046, India

    R. Sakthivel

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  1. Yong Ren
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  2. R. Sakthivel
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Correspondence to Yong Ren.

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This work is supported by the National Natural Science Foundation of China (11871076).

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Ren, Y., Sakthivel, R. Stochastic Differential Equations with Perturbations Driven by G-Brownian Motion. Qual. Theory Dyn. Syst. 19, 74 (2020). https://doi.org/10.1007/s12346-020-00411-3

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  • DOI: https://doi.org/10.1007/s12346-020-00411-3

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