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Almost sure stability of linear stochastic differential equations with jumps
Li, CW; Dong, Z; Situ, R
2002-05-01
Source PublicationPROBABILITY THEORY AND RELATED FIELDS
ISSN0178-8051
Volume123Issue:1Pages:121-155
AbstractUnder 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.
Keywordjump-diffusion invariant measure Lyapunov exponent Fredholm alternative exponential martingale large deviations
DOI10.1007/s004400200198
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000176317300006
PublisherSPRINGER-VERLAG
Citation statistics
Cited Times:19[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17080
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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