Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion

被引：5

作者：

Zhou, Hao ^{[1
]}

Hu, Yaozhong ^{[2
]}

Liu, Yanghui ^{[3
]}

机构：

[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[3] CUNY, Baruch Coll, Dept Math, New York, NY 10010 USA

来源：

BIT NUMERICAL MATHEMATICS | 2023年 / 63卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Backward Euler method; Stochastic differential equation; Malliavin derivative; Strong convergence; Asymptotic error distribution; APPROXIMATION;

D O I：

10.1007/s10543-023-00981-z

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study the traditional backward Euler method for stochastic differential equation driven by fractional Brownian motion whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler scheme is proved to be of order one and this rate is optimal by showing the asymptotic error distribution result. Numerical experiments are performed to validate our claims about the optimality of the rate of convergence.

引用

页数：37

共 20 条

[1]

Abbaszadeh M, 2013, Arxiv, DOI arXiv:1302.5867

[2]

Biagini F, 2008, PROBAB APPL SER, P1

[3]

Brahim B., 2005, REV ROUMAINE MATH PU, V50, P125

[4]

Hairer Ernst., 1996, Solving ordinary differential equations, volume II of Springer Series in Computational Mathematics, 14, VII

[5] Ergodicity of stochastic differential equations driven by fractional Brownian motion [J].

Hairer, M .

ANNALS OF PROBABILITY, 2005, 33 (02) :703-758

[6] Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion [J].

Hong, Jialin ;

Huang, Chuying ;

Kamrani, Minoo ;

Wang, Xu .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (05) :2675-2692

[7]

Hu Y., 2017, Analysis on Gaussian spaces

[8] A singular stochastic differential equation driven by fractional Brownian motion [J].

Hu, Yaozhong ;

Nualart, David ;

Song, Xiaoming .

STATISTICS & PROBABILITY LETTERS, 2008, 78 (14) :2075-2085

[9] RATE OF CONVERGENCE AND ASYMPTOTIC ERROR DISTRIBUTION OF EULER APPROXIMATION SCHEMES FOR FRACTIONAL DIFFUSIONS [J].

Hu, Yaozhong ;

Liu, Yanghui ;

Nualart, David .

ANNALS OF APPLIED PROBABILITY, 2016, 26 (02) :1147-1207

[10]

Hu YZ, 2005, MEM AM MATH SOC, V175, pIII

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