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

2020/04/06 by Xiaobin Sun, Sun, Xiaobin, Longjie Xie +3
Economics, Econometrics and Finance · Physics and Astronomy · Social Sciences · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2004.02595

openalex publication_date 2020/04/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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