Compensated stochastic theta methods for stochastic differential equations with jumps
Compensated stochastic theta methods for stochastic differential equations with jumps
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带跳跃的随机微分方程的补偿随机 theta 方法
DOI：
10.1016/j.apnum.2010.04.012
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发表时间：
2010-09
影响因子：
2.8
通讯作者：
Gan, Siqing
中科院分区：
文献类型：
--
作者：
Wang, Xiaojie;Gan, Siqing
In this paper, a family of compensated stochastic theta methods (CSTM), as opposed to stochastic theta methods (STM) are proposed after the introduction of a compensated Poisson process. These methods are justified to have a strong convergence order of 1/2. Further we investigate mean-square stability of the proposed methods. For a linear test equation, we show that an extension of the deterministic A-stability property holds for CSTM, if and only if 1/2⩽θ⩽1. For a general nonlinear problem, of which the drift term f has a negative one-sided Lipschitz constant and the diffusion terms g,h satisfy global Lipschitz condition, we find that backward Euler method (STM with θ=1) preserves stability under a stepsize constraint, while compensated backward Euler method (CSTM with θ=1) gives a generalization of the deterministic B-stability. Those stability results indicate that CSTM achieve superiority over STM in terms of stability.
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DOI：
10.1007/978-3-540-68829-7_21
发表时间：
2012
期刊：
--
影响因子：
--
作者：
N. Halidias
通讯作者：
N. Halidias
DOI：
10.1017/cbo9780511755323.009
发表时间：
2004
期刊：
--
影响因子：
--
作者：
D. Applebaum
通讯作者：
D. Applebaum
DOI：
10.1007/978-3-662-09947-6
发表时间：
2010-03
期刊：
--
影响因子：
--
作者：
E. Hairer;G. Wanner
通讯作者：
E. Hairer;G. Wanner
DOI：
10.1080/17442509408833885
发表时间：
1994-03
期刊：
Stochastics and Stochastics Reports
影响因子：
--
作者：
D. Talay
通讯作者：
D. Talay
DOI：
10.1007/978-94-011-3712-6
发表时间：
1991
期刊：
--
影响因子：
--
作者：
K. Sobczyk
通讯作者：
K. Sobczyk