Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
| dc.creator | Caballero, M. E. | |
| dc.creator | Chaumont, L. | |
| dc.date | 2004-06-01 | |
| dc.date | 2006-06-30 | |
| dc.date.accessioned | 2026-07-07T06:36:49Z | |
| dc.date.available | 2026-07-07T06:36:49Z | |
| dc.description | Using Lamperti's relationship between Lévy processes and positive self-similar Markov processes (pssMp), we study the weak convergence of the law $\mathbb{P}_x$ of a pssMp starting at $x>0$, in the Skorohod space of càdlàg paths, when $x$ tends to 0. To do so, we first give conditions which allow us to construct a càdlàg Markov process $X^{(0)}$, starting from 0, which stays positive and verifies the scaling property. Then we establish necessary and sufficient conditions for the laws $\mathbb{P}_x$ to converge weakly to the law of $X^{(0)}$ as $x$ goes to 0. In particular, this answers a question raised by Lamperti [Z. Wahrsch. Verw. Gebiete 22 (1972) 205--225] about the Feller property for pssMp at $x=0$. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000611 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0406015 | |
| dc.identifier | http://arxiv.org/abs/math/0406015 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 3, 1012-1034 | |
| dc.identifier | doi:10.1214/009117905000000611 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100211 | |
| dc.subject | Probability | |
| dc.subject | 60G18, 60G51, 60B10 (Primary) | |
| dc.title | Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes | |
| dc.type | text |