Convergence and stability of the split-step composite θ-Milstein method for stochastic delay differential equations

被引：0

作者：

Lu, Yuanqiao ^{[1
]}

Zhang, Haomin ^{[1
,2
]}

Hong, Songyu ^{[1
]}

机构：

[1] Guilin Univ Technol, Sch Sci, Guilin 541006, Guangxi, Peoples R China

[2] Guilin Univ Technol, Guangxi Coll & Univ Key Lab Appl Stat, Guilin 541000, Guangxi, Peoples R China

来源：

INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL | 2024年 / 12卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Stochastic delay differential equation; Convergence; Mean-square stability; Split-step composite theta-Milstein method; Milstein; EXPONENTIAL STABILITY; EULER METHOD; APPROXIMATIONS;

D O I：

10.1007/s40435-023-01253-y

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This research analyzes split-step composite theta-Milstein (SSCTM) method based on stochastic delay differential equations, with particular focuses on examining its convergence and stability. We prove SSCTM method converges with strong order 1. Sufficient conditions for stability are given. Further, the regions in which SSCTM method exhibits stability are investigated. Numerical simulations validate our theoretical part.

引用

页码：1302 / 1313

页数：12

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