Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by Lévy processes

2022/08/16 by Shi, Yinghui, Sun, Xiaobin, Wang, Liqiong +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2208.07560

Abstract

In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by Lévy 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 Lévy processes, which seems new in the existing literature.

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