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February 2022 Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process
Xiaobin Sun, Longjie Xie, Yingchao Xie
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Bernoulli 28(1): 343-369 (February 2022). DOI: 10.3150/21-BEJ1345

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 11/α and 1 respectively. We show, by a simple example, that 11/α is the optimal strong convergence rate.

Funding Statement

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.

Acknowledgements

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.

Citation

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Xiaobin Sun. Longjie Xie. Yingchao Xie. "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

Information

Received: 1 April 2020; Revised: 1 October 2020; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1345

Keywords: averaging principle , Convergence rates , slow–fast system , α-stable process

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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