A note on the supremum of a stable process

Autor:	Doney, R. A.
Rok vydání:	2007
Předmět:	Mathematics - Probability 60J30 60F15 (Primary)
Druh dokumentu:	Working Paper
Popis:	If $X$ is a spectrally positive stable process of index $\alpha\in(1,2)$ whose L\'{e}vy measure has density $cx^{-\alpha-1}$ on $(0,\infty),$ and $S_1=\sup_{0x)\backsim c\alpha^{-1}x^{-\alpha}$ 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 $s(x)\backsim cx^{-(\alpha+1)}$ as $x\to\infty.$ Comment: 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)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0712.3414 Zobrazit plný text záznamu View this record from Arxiv