Product expansion for stochastic jump diffusions and its application to numerical approximation

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	Product expansion for stochastic jump diffusions and its application to numerical approximation
	Liu, XQ ; Li, CW
	1999-08-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	108 期号:1-2 页码:1-17
摘要	We derive a product expansion of the exponential Lie series in terms of a Philip Hall basis for the Chen series corresponding to the stochastic jump diffusion as in Sussmann (in: C.I. Byrnes and A. Lindquist (Eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, Amsterdam, 1986, pp. 323-335) for the deterministic case. Based on the expansion, we establish the Stratonovich-Taylor-Hall (STH) schemes such that each scheme involves only the minimum number of multiple stochastic integrals, which can be regarded as systems of stochastic differential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy. Mean-square convergence of the STH schemes is shown and numerical examples are provided to illustrate the results. (C) 1999 Elsevier Science B.V. All rights reserved. MSG: primary 65U05; secondary 60H10, 60J65; 60G55; 41A58.
关键词	jump diffusion multiple stochastic integral Stratonovich-Taylor expansion exponential Lie series Philip Hall basis shuffle product mean square convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000081945900001
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14910
专题	中国科学院数学与系统科学研究院
作者单位	1.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong 2.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, XQ,Li, CW. Product expansion for stochastic jump diffusions and its application to numerical approximation[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,1999,108(1-2):1-17.
APA	Liu, XQ,&Li, CW.(1999).Product expansion for stochastic jump diffusions and its application to numerical approximation.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,108(1-2),1-17.
MLA	Liu, XQ,et al."Product expansion for stochastic jump diffusions and its application to numerical approximation".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 108.1-2(1999):1-17.