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Strong and weak convergence rates for slow-fast stochastic differential equations driven by $α$-stable process
Xiaobin Sun, Longjie Xie, Yingchao Xie · 2020-04-06 · via math.PR updates on arXiv.org

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 $α\in(1,2)$. 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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