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.
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页码：3663 / 3682
页数：20
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