Sinai's condition for real valued Lévy processes
| dc.creator | Rivero, Victor | |
| dc.date | 2005-05-24 | |
| dc.date.accessioned | 2026-07-07T05:20:13Z | |
| dc.date.available | 2026-07-07T05:20:13Z | |
| dc.description | We prove that the upward ladder height subordinator $H$ associated to a real valued Lévy process $ξ$ has Laplace exponent $ϕ$ that varies regularly at $\infty$ (resp. at 0) if and only if the underlying Lévy process $ξ$ satisfies Sinai's condition at 0 (resp. at $\infty$). Sinai's condition for real valued Lévy processes is the continuous time analogue of Sinai's condition for random walks. We provide several criteria in terms of the characteristics of $ξ$ to determine whether or not it satisfies Sinai's condition. Some of these criteria are deduced from tail estimates of the Lévy measure of $H,$ here obtained, and which are analogous to the estimates of the tail distribution of the ladder height random variable of a random walk which are due to Veraverbeke and Grübel | |
| dc.description | 26 pages, 24 Mai 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0505495 | |
| dc.identifier | http://arxiv.org/abs/math/0505495 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75296 | |
| dc.subject | Probability | |
| dc.subject | MSC: 60G30 (60G51) | |
| dc.title | Sinai's condition for real valued Lévy processes | |
| dc.type | text |