Asymptotics for first-passage times of Lévy processes and random walks
| dc.creator | Denisov, Denis | |
| dc.creator | Shneer, Vsevolod | |
| dc.date | 2007-12-05 | |
| dc.date.accessioned | 2026-07-07T08:47:26Z | |
| dc.date.available | 2026-07-07T08:47:26Z | |
| dc.description | We study the exact asymptotics for the distribution of the first time $τ_x$ a Lévy process $X_t$ crosses a negative level $-x$. We prove that $\mathbf P(τ_x>t)\sim V(x)\mathbf P(X_t\ge 0)/t$ as $t\to\infty$ for a certain function $V(x)$. Using known results for the large deviations of random walks we obtain asymptotics for $\mathbf P(τ_x>t)$ explicitly in both light and heavy tailed cases. We also apply our results to find asymptotics for the distribution of the busy period in an M/G/1 queue. | |
| dc.identifier | https://arxiv.org/abs/0712.0728 | |
| dc.identifier | http://arxiv.org/abs/0712.0728 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143599 | |
| dc.subject | Probability | |
| dc.subject | 60G50; 60G51 | |
| dc.title | Asymptotics for first-passage times of Lévy processes and random walks | |
| dc.type | text |