Abstract
In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the equation \(X_t=x+B_t^H+\int _0^t b(X_s)ds\) where \(\{B_t^H, t\in [0,T]\}\) is a fractional Brownian motion with Hurst parameter \(H\in \big (\frac{1}{2},1\big )\). Based on the techniques of Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence.
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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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Communicated by Eric A. Carlen.
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Son, T.C. The Rate of Convergence for the Smoluchowski-Kramers Approximation for Stochastic Differential Equations with FBM. J Stat Phys 181, 1730–1745 (2020). https://doi.org/10.1007/s10955-020-02643-8
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DOI: https://doi.org/10.1007/s10955-020-02643-8
Keywords
- Smoluchowski–Kramers approximation
- Fractional Brownian motion
- Total variation distance
- Malliavin calculus