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

共 50 条

[21] A RANDOMIZED MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-DIFFERENTIABLE DRIFT COEFFICIENTS
Kruse, Raphael
Wu, Yue
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3475 - 3502
[22] The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients
Liu, Wei
Mao, Xuerong
Wu, Yue
APPLIED NUMERICAL MATHEMATICS, 2023, 184 : 137 - 150
[23] On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching
Kumar, Chaman
Kumar, Tejinder
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 377
[24] An analytic approximation of solutions of stochastic differential delay equations with Markovian switching
Bao, Jianhai
Hou, Zhenting
MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (9-10) : 1379 - 1384
[25] A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients
Bahlali, Khaled
Hakassou, Antoine
Ouknine, Youssef
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2015, 87 (05) : 806 - 847
[26] Numerical solutions of neutral stochastic functional differential equations with Markovian switching
Hu, Yuru
Chen, Huabin
Yuan, Chenggui
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
[27] Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
Mao, Xuerong
Szpruch, Lukasz
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2013, 85 (01) : 144 - 171
[28] On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients
Jian, Jiamin
Song, Qingshuo
Wang, Xiaojie
Zhang, Zhongqiang
Zhao, Yuying
AUTOMATICA, 2025, 177
[29] LEAST SQUARES ESTIMATORS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING
Zhen, Yuhang
Xi, Fubao
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (07): : 4068 - 4086
[30] Exponential ergodicity for stochastic functional differential equations with Markovian switching
Zhai, Yafei
Xi, Fubao
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 534 (01)

← 1 2 3 4 5 →