An Explicit Split-Step Truncated Milstein Method for Stochastic Differential Equations
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS(2023)
摘要
In this paper, we propose an explicit split-step truncated Milstein method for stochastic differential equations (SDEs) with commutative noise. We discuss the mean-square convergence properties of the new method for numerical solutions of a class of highly nonlinear SDEs in a finite time interval. As a result, we show that the strong convergence rate of the new method can be arbitrarily close to one under some additional conditions. Finally, we use an illustrative example to highlight the advantages of our new findings in terms of both stability and accuracy compared to the results in Guo et al. (2018).
更多查看译文
关键词
Stochastic differential equations,Non-globally Lipschitz conditions,strong convergence rate,Truncated Milstein method,Split-step methods
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要