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 . We prove that the strong and weak convergence order are and 1 respectively. We show, by a simple example, that is the optimal strong convergence rate.
This work is supported by the NNSF of China (12090011, 12071186, 11771187, 11931004) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
We would like to thank Professor Renming Song for useful discussion, and the referees for carefully reading the manuscript and providing many suggestions and comments.
"Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process." Bernoulli 28 (1) 343 - 369, February 2022. https://doi.org/10.3150/21-BEJ1345