A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping

随机变分波方程的Smoluchowski-Kramers近似

A Smoluchowski-Kramers approximation for the stochastic variational wave equation

研究一维周期变分波方程在状态依赖阻尼和加性噪声下的Smoluchowski-Kramers近似，证明弱“耗散”解收敛到随机拟线性抛物方程的解。

Asymptotics for scaled Kramers-Smoluchowski equations in several dimensions with general potentials

In this paper, we generalize the results of Evans and Tabrizian, by deriving asymptotics for the time-rescaled Kramers-Smoluchowski equations, in the case of a general non-symmetric potential function with multiple wells. The asymptotic limit is described by a system of reaction-diffusion equations whose coefficients are determined by the Kramers constants at the saddle points of the potential function and the Hessians of the potential function at global minima.

Smoluchowski-Kramers近似下随机偏微分方程的强收敛与弱收敛速率

Strong and weak rates of convergence in the Smoluchowski--Kramers approximation for stochastic partial differential equations

本文研究了在小质量极限下随机阻尼半线性波动方程的Smoluchowski-Kramers近似收敛速率，根据驱动Wiener过程的正则性，强收敛和弱收敛速率分别为1或1/2和1。

二维奇异随机波动方程的Smoluchowski-Kramers近似

Smoluchowski-Kramers approximation for singular stochastic wave equations in two dimensions

该研究针对二维环面上带多项式与正弦非线性项的阻尼随机波动方程，证明当小参数趋于零时其解收敛到随机量子化方程的解，且两种非线性情形下该近似在任意大时间均成立，突破了多项式情形波动方程缺乏全局适定性的限制。

A semiclassical approach to the Kramers--Smoluchowski equation

We consider the Kramers--Smoluchowski equation at a low temperature regime and show how semiclassical techniques developed for the study of the Witten Laplacian and Fokker--Planck equation provide quantitative results. This equation comes from molecular dynamics and temperature plays the role of a semiclassical paramater. The presentation is self-contained in the one dimensional case, with pointers to the recent paper \cite{Mi16} for results needed in higher dimensions. One purpose of this note is to provide a simple introduction to semiclassical methods in this context.

Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations

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.