Convergence and stability of the compensated split-step θ-method for stochastic differential equations with jumps

被引：4
|
作者：
Tan, Jianguo [1 ]
Mu, Zhiming [2 ]
Guo, Yongfeng [1 ]
机构：
[1] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China
[2] Tianjin Agr Univ, Coll Basic Sci, Tianjin 300384, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2014年
基金：
中国国家自然科学基金;
关键词：
stochastic differential equations; Poisson jumps; compensated split-step theta-method; convergence; mean-square stability; APPROXIMATIONS; DIFFUSION;
D O I：
10.1186/1687-1847-2014-209
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a new compensated split-step theta (CSS theta) method for stochastic differential equations with jumps (SDEwJs). First, it is proved that the proposed method is convergent with strong order 1/2 in the mean-square sense. Then the condition of the mean-square (MS) stability of the CSS theta method is obtained. Finally, some scalar test equations are simulated to verify the results obtained from theory, and a comparison between the compensated stochastic theta (CST) method by Wang and Gan (Appl. Numer. Math. 60:877-887, 2010) and CSS theta is analyzed. Meanwhile, the results show the higher efficiency of the CSS theta method.
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页数：19
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