Strong and weak convergence rates for slow-fast stochastic differential equations driven by α-stable process

被引：19

作者：

Sun, Xiaobin ^{[1
]}

Xie, Longjie ^{[1
]}

Xie, Yingchao ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221000, Jiangsu, Peoples R China

来源：

BERNOULLI | 2022年 / 28卷 / 01期

关键词：

Averaging principle; alpha-stable process; slow-fast system; convergence rates; AVERAGING PRINCIPLE; DIFFUSION-APPROXIMATION; POISSON EQUATION; SYSTEMS; ORDER;

D O I：

10.3150/21-BEJ1345

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study the averaging principle for a class of stochastic differential equations driven by alpha-stable processes with slow and fast time-scales, where alpha is an element of (1, 2). We prove that the strong and weak convergence order are 1 - 1/alpha and 1 respectively. We show, by a simple example, that 1 - 1/alpha is the optimal strong convergence rate.

引用

页码：343 / 369

页数：27

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