Convergence rate of numerical solutions to SFDEs with jumps

被引：34

作者：

Bao, Jianhai ^{[1
]}

Boettcher, Bjoern ^{[2
]}

Mao, Xuerong ^{[3
]}

Yuan, Chenggui ^{[1
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Tech Univ Dresden, Dept Math, D-01062 Dresden, Germany

[3] Univ Strathclyde, Dept Stat & Modelling Sci, Glasgow G1 1XH, Lanark, Scotland

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 236卷 / 02期

关键词：

Euler-Maruyama; Local Lipschitz condition; SFDE; Convergence rate; Poisson process; STOCHASTIC DIFFERENTIAL-EQUATIONS; EULER;

D O I：

10.1016/j.cam.2011.05.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are interested in numerical solutions of stochastic functional differential equations with jumps. Under a global Lipschitz condition, we show that the pth-moment convergence of Euler-Maruyama numerical solutions to stochastic functional differential equations with jumps has order 1/p for any p >= 2. This is significantly different from the case of stochastic functional differential equations without jumps, where the order is 1/2 for any p >= 2. It is therefore best to use the mean-square convergence for stochastic functional differential equations with jumps. Moreover, under a local Lipschitz condition, we reveal that the order of mean-square convergence is close to 1/2, provided that local Lipschitz constants, valid on balls of radius j, do not grow faster than logj. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：119 / 131

页数：13

共 13 条

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[13] A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations
Yuan, Chenggui
Mao, Xuerong
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, 26 (02) : 325 - 333

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