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A Berry–Esseen Bound in the Smoluchowski–Kramers Approximation

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Abstract

In this paper, we use the Kolmogorov distance to investigate the Smoluchowski–Kramers approximation for stochastic differential equations. We obtain an explicit Berry–Esseen error bound for the rate of convergence. Our main tools are the techniques of Malliavin calculus.

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Acknowledgements

The authors would like to thank the anonymous referee for their valuable comments for improving the paper. This research was funded by Viet Nam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2019.08.

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Authors and Affiliations

  1. Department of Foundation, Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, Vietnam

    Nguyen Van Tan

  2. Department of Mathematics, VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Nguyen Tien Dung

  3. Department of Mathematics, FPT University, Hoa Lac High Tech Park, Hanoi, Vietnam

    Nguyen Tien Dung

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  1. Nguyen Van Tan
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  2. Nguyen Tien Dung
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Correspondence to Nguyen Tien Dung.

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Communicated by Eric A. Carlen.

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Van Tan, N., Dung, N.T. A Berry–Esseen Bound in the Smoluchowski–Kramers Approximation. J Stat Phys 179, 871–884 (2020). https://doi.org/10.1007/s10955-020-02564-6

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  • DOI: https://doi.org/10.1007/s10955-020-02564-6

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