Compensated θ-Milstein methods for stochastic differential equations with Poisson jumps

被引：9

作者：

Ren, Quanwei ^{[1
]}

Tian, Hongjiong ^{[2
]}

机构：

[1] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Henan, Peoples R China

[2] Shanghai Normal Univ, Dept Math, 100 Guilin Rd, Shanghai 200234, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 150卷 / 27-37期

基金：

上海市自然科学基金; 中国国家自然科学基金;

关键词：

Compensated theta-Milstein methods; Mean-square convergence; Asymptotic mean-square stability; Poisson jump; NUMERICAL-METHODS; APPROXIMATIONS; CONVERGENCE; STABILITY;

D O I：

10.1016/j.apnum.2019.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with numerical methods for solving stochastic differential equations with Poisson-driven jumps. We construct a class of compensated theta-Milstein methods and study their mean-square convergence and asymptotic mean-square stability. Sufficient and necessary conditions for the asymptotic mean-square stability of the compensated theta-Milstein methods when applied to a scalar linear test equation are derived. We compare the asymptotic mean-square stability region of the linear test equation with that of the compensated theta-Milstein methods with different theta values. Numerical results are given to verify our theoretical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：27 / 37

页数：11

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