THE TRUNCATED MILSTEIN METHOD FOR SUPER-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING

被引：2

作者：

Zhan, Weijun ^{[1
]}

Guo, Qian ^{[2
]}

Cong, Yuhao ^{[3
]}

机构：

[1] Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Shanghai Customs Coll, Shanghai 201204, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年 / 27卷 / 07期

关键词：

Milstein method; Khasminskii-type condition; strong convergence; Markovian switching; Stochastic differential equation; EULER-MARUYAMA METHOD; STRONG-CONVERGENCE; SDES;

D O I：

10.3934/dcdsb.2021201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, to approximate the sup er-linear stochastic differ-ential equations modulated by a Markov chain, we investigate a truncated Milstein method with convergence order 1 in the mean-square sense. Under Khasminskii-type conditions, we establish the convergence result by employ-ing a relationship between local and global errors. Finally, we confirm the convergence rate by a numerical example.

引用

页码：3663 / 3682

页数：20

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