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
收藏
页码：27 / 37
页数：11
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