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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Bibliographic Details
Published inJournal of statistical physics Vol. 179; no. 4; pp. 871 - 884
Main Authors Van Tan, Nguyen, Dung, Nguyen Tien
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2020
Springer
Springer Nature B.V
Subjects
Approximation
Differential equations
Mathematical analysis
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Berry–Esseen bound
60H07
Smoluchowski–Kramers approximation
82C31
Malliavin calculus
60H15
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Summary: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