Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by L\'evy processes

Yinghui Shi; Xiaobin Sun; Liqiong Wang; Yingchao Xie

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arXiv · 2208.07560

Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by L\'evy processes

Yinghui Shi·Xiaobin Sun·Liqiong Wang·Yingchao Xie

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Abstract

In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by L\'evy processes. The optimal strong convergence order 1/2 is obtained by studying the regularity estimates for the solution of Poisson equation with polynomial growth coefficients, and the optimal weak convergence order 1 is got by using the technique of Kolmogorov equation. The main contribution is that the obtained results can be applied to a class of multi-scale stochastic differential equations with monotonicity coefficients, as well as the driven processes can be the general L\'evy processes, which seems new in the existing literature.

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Yinghui Shi, Xiaobin Sun, Liqiong Wang, Yingchao Xie. 2022-08-16. Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by L\'evy processes. https://arxiv.org/abs/2208.07560

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