KMS Of Academy of mathematics and systems sciences, CAS
Almost sure stability of linear stochastic differential equations with jumps | |
Li, CW; Dong, Z; Situ, R | |
2002-05-01 | |
Source Publication | PROBABILITY THEORY AND RELATED FIELDS |
ISSN | 0178-8051 |
Volume | 123Issue:1Pages:121-155 |
Abstract | 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. |
Keyword | jump-diffusion invariant measure Lyapunov exponent Fredholm alternative exponential martingale large deviations |
DOI | 10.1007/s004400200198 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000176317300006 |
Publisher | SPRINGER-VERLAG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/17080 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
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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