A Berry–Esseen Bound in the Smoluchowski–Kramers Approximation

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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Bibliographische Detailangaben
Veröffentlicht in:	Journal of statistical physics 2020-05, Vol.179 (4), p.871-884
Hauptverfasser:	Van Tan, Nguyen, Dung, Nguyen Tien
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Differential equations Mathematical analysis Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical
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Beschreibung
Zusammenfassung:	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.
ISSN:	0022-4715 1572-9613
DOI:	10.1007/s10955-020-02564-6