Quantitative approximation of stochastic kinetic equations: from discrete to continuum

Zimo Hao, Khoa Lê, Chengcheng Ling
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Abstract

We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for the kinetic type stochastic differential equations (SDEs) (also known as second order SDEs) with singular coefficients in both weak and strong probabilistic senses. We show that when the drift exhibits a relatively low regularity compared to the state of the art, the singular system is well-defined both in the weak and strong probabilistic senses. Meanwhile, the corresponding tamed EM scheme is shown to converge at the rate of 1/2 in both the weak and the strong senses.
随机动力学方程的定量近似:从离散到连续
我们研究了在弱概率和强概率意义上具有奇异系数的动力学型随机微分方程(SDE)(也称为二阶随机微分方程)的通用驯服欧拉-马鲁山(EM)方案的收敛性。我们的研究表明,当漂移表现出与现有技术相比相对较低的正则性时,奇异系统在弱概率和强概率意义上都定义良好。同时,相应的驯化 EMscheme 在弱概率和强概率下都能以 1/2 的速率收敛。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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