论文标题
随机微分方程的修饰截短米尔斯坦方法的收敛性和指数稳定性
Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations
论文作者
论文摘要
在本文中，我们开发了一种称为修改的截短米尔斯坦方法的新的显式方案，该方案是由Guo（2018）提出的截短的米尔斯坦方法和LAN（2018）介绍的修改后的Euler-Maruyama方法所提出的。我们在局部界限和khasminskii型条件下获得了该方案的强收敛，这些条件相对较弱，比现有结果较弱，我们证明，在给定条件下，收敛速率可以任意接近1。此外，还考虑了该方案的指数稳定性，而Guo（2018）中引入的截短米尔斯坦方法不可能。提供了三个数值实验来支持我们的结论。
In this paper, we develop a new explicit scheme called modified truncated Milstein method which is motivated by truncated Milstein method proposed by Guo (2018) and modified truncated Euler-Maruyama method introduced by Lan (2018). We obtain the strong convergence of the scheme under local boundedness and Khasminskii-type conditions, which are relatively weaker than the existing results, and we prove that the convergence rate could be arbitrarily close to 1 under given conditions. Moreover, exponential stability of the scheme is also considered while it is impossible for truncated Milstein method introduced in Guo(2018). Three numerical experiments are offered to support our conclusions.
