论文标题
由Lévy过程驱动的单调系数的多尺度SDE的渐近行为
Asymptotic behavior for multi-scale SDEs with monotonicity coefficients driven by Lévy processes
论文作者
论文摘要
在本文中，我们研究了由Lévy过程驱动的多尺度随机微分方程的渐近行为。最佳的强收敛顺序1/2是通过研究使用多项式生长系数的泊松方程溶液的规律性估计来获得的，并且通过使用Kolmogorov方程的技术获得最佳的弱收敛顺序1。主要的贡献是，获得的结果可以应用于具有单调性系数的一类多尺度随机微分方程，以及驱动的过程可以是一般的lévy过程，在现有文献中似乎是新的。
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.
