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

Advances in Difference Equations

Zhiming Mu¹  Yongfeng Guo²  Jianguo Tan² 

[1] College of Basic Science, Tianjin Agricultural University, Tianjin, China;Department of Mathematics, Tianjin Polytechnic University, Tianjin, China

关键词: stochastic differential equations;    Poisson jumps;    compensated split-step θ-method;    convergence;    mean-square stability;   

DOI  :  10.1186/1687-1847-2014-209

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we develop a new compensated split-step θ (CSSθ) 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 CSSθ 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 CSSθ is analyzed. Meanwhile, the results show the higher efficiency of the CSSθ method.

【 授权许可】

CC BY