Double-implicit and split two-step Milstein schemes for stochastic differential equations

doi:10.1080/00207160.2015.1081182

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	Double-implicit and split two-step Milstein schemes for stochastic differential equations
	Jiang, Fengze 1; Zong, Xiaofeng 2; Yue, Chao 1; Huang, Chengming 1
	2016-12-01
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
卷号	93 期号:12 页码:1987-2011
摘要	In this work, we propose two classes of two-step Milstein-type schemes : the double-implicit Milstein scheme and the split two-step Milstein scheme, to solve stochastic differential equations (SDEs). Our results reveal that the two new schemes are strong convergent with order one. Moreover, with a restriction on stepsize, these two schemes can preserve the exponential mean square stability of the original SDEs, and the decay rate of numerical solution will converge to the decay rate of the exact solution. Numerical experiments are performed to confirm our theoretic findings.
关键词	double-implicit Milstein method split two-step Milstein method strong convergence exponential mean square stability
DOI	10.1080/00207160.2015.1081182
语种	英语
资助项目	NSF of China[91130003] ; NSF of China[11371157] ; NSF of China[1422110] ; NSF of China[61473125] ; NSF of China[11301198] ; Fundamental Research Funds for the Central Universities[2013TS137]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000389437900002
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24285
专题	中国科学院数学与系统科学研究院
通讯作者	Zong, Xiaofeng
作者单位	1.Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jiang, Fengze,Zong, Xiaofeng,Yue, Chao,et al. Double-implicit and split two-step Milstein schemes for stochastic differential equations[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2016,93(12):1987-2011.
APA	Jiang, Fengze,Zong, Xiaofeng,Yue, Chao,&Huang, Chengming.(2016).Double-implicit and split two-step Milstein schemes for stochastic differential equations.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,93(12),1987-2011.
MLA	Jiang, Fengze,et al."Double-implicit and split two-step Milstein schemes for stochastic differential equations".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 93.12(2016):1987-2011.