论文标题
平均场随机微分方程的Smoluchowski-Kramer近似中的收敛速率
Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations
论文作者
论文摘要
在本文中，我们研究了一个二阶平均田间随机微分系统，该系统描述了粒子在时间依赖力，摩擦，平均场相互作用以及空间和时间依赖性随机噪声的影响下的运动。使用Malliavin微积分的技术，我们在$ L^p $距离的零质量限制（Smoluchowski-Kramers近似）中建立了明显的收敛速率，并且在位置过程的总变化距离，速度过程和重新尺寸的速度速度过程中，对相应的限制过程进行了重新尺寸的速度。
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.
