Strong rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero

被引：7

作者：

Benabdallah, Mohsine ^{[1
]}

Hiderah, Kamal ^{[2
]}

机构：

[1] Univ Ibn Tofail, Dept Math, Fac Sci, Kenitra, Morocco

[2] Univ Aden, Dept Math, Fac Sci, Aden, Yemen

来源：

MONTE CARLO METHODS AND APPLICATIONS | 2018年 / 24卷 / 04期

关键词：

Euler-Maruyama approximation; strong convergence; stochastic differential equations; local time;

D O I：

10.1515/mcma-2018-2021

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We present the Euler-Maruyama approximation for one-dimensional stochastic differential equations involving the local time at point zero. Also, we prove the strong convergence of the Euler-Maruyama approximation whose both drift and diffusion coefficients are Lipschitz. After that, we generalize to the non-Lipschitz case.

引用

页码：249 / 262

页数：14

共 50 条

[41] Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation
Milosevic, Marija
MATHEMATICAL AND COMPUTER MODELLING, 2013, 57 (3-4) : 887 - 899
[42] An Euler-Maruyama method for Caputo-Hadamard fractional stochastic differential equations on exponential meshes and its fast approximation
Li, Min
Guo, Shangjiang
Hu, Peng
Song, Haiyan
NUMERICAL ALGORITHMS, 2024, : 573 - 601
[43] Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay
Chengjian Zhang
Ying Xie
ScienceChina(Mathematics), 2019, 62 (03) : 597 - 616
[44] Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay
Zhang, Chengjian
Xie, Ying
SCIENCE CHINA-MATHEMATICS, 2019, 62 (03) : 597 - 616
[45] Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise
Yang, Zhiwei
Zheng, Xiangcheng
Zhang, Zhongqiang
Wang, Hong
CHAOS SOLITONS & FRACTALS, 2021, 142
[46] Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay
Chengjian Zhang
Ying Xie
Science China Mathematics, 2019, 62 : 597 - 616
[47] Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations
Liu, Wei
Mao, Xuerong
Tang, Jingwen
Wu, Yue
APPLIED NUMERICAL MATHEMATICS, 2020, 153 : 66 - 81
[48] Convergence and stability of modified partially truncated Euler-Maruyama method for nonlinear stochastic differential equations with Holder continuous diffusion coefficient
Yang, Hongfu
Huang, Jianhua
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 404
[49] ON ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING THE MAXIMUM PROCESS
Belfadli, R.
Hamadene, S.
Ouknine, Y.
STOCHASTICS AND DYNAMICS, 2009, 9 (02) : 277 - 292
[50] Semi-implicit Euler-Maruyama method for non-linear time-changed stochastic differential equations
Deng, Chang-Song
Liu, Wei
BIT NUMERICAL MATHEMATICS, 2020, 60 (04) : 1133 - 1151

← 1 2 3 4 5 →