Almost sure stability of linear stochastic differential equations with jumps

doi:10.1007/s004400200198

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	Almost sure stability of linear stochastic differential equations with jumps
	Li, CW ; Dong, Z; Situ, R
	2002-05-01
发表期刊	PROBABILITY THEORY AND RELATED FIELDS
ISSN	0178-8051
卷号	123 期号:1 页码:121-155
摘要	Under the nondegenerate condition as in the diffusion case, see [14, 21, 6], the linear stochastic jump-diffusion process projected on the unit sphere is a strong Feller process and has a unique invariant measure which is also ergodic using the relation between the transition probabilities of jump-diffusions and the corresponding diffusions due to [22]. The unique deterministic Lyapunov exponent can be represented by the Furstenberg-Khas'minskii formula as an integral over the sphere or the projective space with respect to the ergodic invariant measure so that the almost sure asymptotic stability of linear stochastic systems with jumps depends on its sign. The critical case of zero Lyapunov exponent is discussed and a large deviations result for asymptotically stable systems is further investigated. Several examples are treated for illustration.
关键词	jump-diffusion invariant measure Lyapunov exponent Fredholm alternative exponential martingale large deviations
DOI	10.1007/s004400200198
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000176317300006
出版者	SPRINGER-VERLAG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17080
专题	应用数学研究所
通讯作者	Li, CW
作者单位	1.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China 3.Zhongshan Univ, Dept Math, Guangzhou 510275, Peoples R China
推荐引用方式 GB/T 7714	Li, CW,Dong, Z,Situ, R. Almost sure stability of linear stochastic differential equations with jumps[J]. PROBABILITY THEORY AND RELATED FIELDS,2002,123(1):121-155.
APA	Li, CW,Dong, Z,&Situ, R.(2002).Almost sure stability of linear stochastic differential equations with jumps.PROBABILITY THEORY AND RELATED FIELDS,123(1),121-155.
MLA	Li, CW,et al."Almost sure stability of linear stochastic differential equations with jumps".PROBABILITY THEORY AND RELATED FIELDS 123.1(2002):121-155.