A note on the supremum of a stable process
| dc.creator | Doney, R. A. | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T08:51:49Z | |
| dc.date.available | 2026-07-07T08:51:49Z | |
| dc.description | If $X$ is a spectrally positive stable process of index $α\in(1,2)$ whose Lévy measure has density $cx^{-α-1}$ on $(0,\infty),$ and $S_1=\sup_{0<t\leq1}X_t,$ it is known that $P(S_1>x)\backsim cα^{-1}x^{-α}$ as $x\to\infty.$ It is also known that $S_1$has a continuous density, $s$ say. The point of this note is to show that $s(x)\backsim cx^{-(α+1)}$ as $x\to\infty.$ | |
| dc.description | To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm) | |
| dc.identifier | https://arxiv.org/abs/0712.3414 | |
| dc.identifier | http://arxiv.org/abs/0712.3414 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145069 | |
| dc.subject | Probability | |
| dc.subject | 60J30, 60F15 (Primary) | |
| dc.title | A note on the supremum of a stable process | |
| dc.type | text |