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

Xiaobin Sun; Longjie Xie; Yingchao Xie

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arXiv · 2004.02595

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

Xiaobin Sun·Longjie Xie·Yingchao Xie

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Abstract

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 $\alpha\in(1,2)$. 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.

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Xiaobin Sun, Longjie Xie, Yingchao Xie. 2020-04-06. Strong and weak convergence rates for slow-fast stochastic differential equations driven by $\alpha$-stable process. https://arxiv.org/abs/2004.02595

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