Almost sure stability of linear stochastic differential equations with jumps

Autor:	C. W. Li, Zhao Dong, R. Situ
Rok vydání:	2002
Předmět:	Statistics and Probability Mathematical analysis Lyapunov exponent Feller process Stochastic differential equation symbols.namesake Linear differential equation Stability theory symbols Ergodic theory Invariant measure Statistics Probability and Uncertainty Jump process Analysis Mathematics
Zdroj:	Probability Theory and Related Fields. 123:121-155
ISSN:	1432-2064 0178-8051
DOI:	10.1007/s004400200198
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::88e183671766b20f6c9e42e4117d845d https://doi.org/10.1007/s004400200198 Zobrazit plný text záznamu Plný text ve formátu PDF