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
收藏
页码：3663 / 3682
页数：20
相关论文
共 50 条
  • [31] A positivity preserving Milstein-type method for stochastic differential equations with positive solutions
    Hu, Xingwei
    Wang, Mengjie
    Dai, Xinjie
    Yu, Yanyan
    Xiao, Aiguo
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 449
  • [32] Stability analysis of stochastic differential equations with Markovian switching
    Zhu, Fubo
    Han, Zhengzhi
    Zhang, Junfeng
    SYSTEMS & CONTROL LETTERS, 2012, 61 (12) : 1209 - 1214
  • [33] SMOOTHNESS OF DENSITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING
    Hu, Yaozhong
    Nualart, David
    Sun, Xiaobin
    Xie, Yingchao
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3615 - 3631
  • [34] Tamed-Euler method for hybrid stochastic differential equations with Markovian switching
    Nguyen, Dung T.
    Nguyen, Son L.
    Hoang, Tuan A.
    Yin, George
    NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2018, 30 : 14 - 30
  • [35] Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching
    Yuan, CG
    Mao, XR
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2004, 64 (02) : 223 - 235
  • [36] An analysis of stability of milstein method for Stochastic differential equations with delay
    Wang, Zhiyong
    Zhang, Chengjian
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (9-10) : 1445 - 1452
  • [37] Numerical solutions of neutral stochastic functional differential equations with Markovian switching
    Yuru Hu
    Huabin Chen
    Chenggui Yuan
    Advances in Difference Equations, 2019
  • [38] The modified truncated Euler-Maruyama method for stochastic differential equations with concave diffusion coefficients
    Tang, Yiyi
    Mao, Xuerong
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 440
  • [39] Approximation of the Likelihood Function for Stochastic Differential Equations with Markovian Switching
    Zhen, Yuhang
    MARKOV PROCESSES AND RELATED FIELDS, 2022, 28 (04) : 527 - 546
  • [40] General decay stability of stochastic differential equations with Markovian switching
    Deng, F.-Q. (aufqdeng@scut.edu.cn), 1600, South China University of Technology (40): : 102 - 108
12345