Abstract
In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent stochastic noise. Using techniques from Malliavin calculus, we establish explicit rates of convergence in the zero-mass limit (Smoluchowski-Kramers approximation) in the \(L^p\)-distances and in the total variation distance for the position process, the velocity process and a re-scaled velocity process to their corresponding limiting processes.
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Research of MHD was supported by EPSRC Grants EP/W008041/1 and EP/V038516/1.
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Son, T.C., Le, D.Q. & Duong, M.H. Rate of Convergence in the Smoluchowski-Kramers Approximation for Mean-field Stochastic Differential Equations. Potential Anal 60, 1031–1065 (2024). https://doi.org/10.1007/s11118-023-10078-5
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DOI: https://doi.org/10.1007/s11118-023-10078-5
Keywords
- Smoluchowski-Kramers approximation
- Stochastic differential by mean-field
- Total variation distance
- Malliavin calculus