Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by L\'evy processes
Probability
2023-09-26 v2
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.
Cite
@article{arxiv.2208.07560,
title = {Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by L\'evy processes},
author = {Yinghui Shi and Xiaobin Sun and Liqiong Wang and Yingchao Xie},
journal= {arXiv preprint arXiv:2208.07560},
year = {2023}
}
Comments
39 pages. To appear in Potential Analysis