On exit time of stable processes

被引：7

作者：

Graczyk, Piotr ^{[2
]}

Jakubowski, Tomasz ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

[2] Univ Angers, Lab Math LAREMA, F-49045 Angers 01, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 01期

关键词：

Stable process; Exit time; EXTREMA; MAXIMA;

D O I：

10.1016/j.spa.2011.10.004

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the exit time tau = tau((0,infinity)) for 1-dimensional strictly stable processes and express its Laplace transform at t(alpha) as the Laplace transform of a positive random variable with explicit density. Consequently, tau satisfies some multiplicative convolution relations. For some stable processes, e.g. for the symmetric 2/3-stable process, explicit formulas for the Laplace transform and the density of tau are obtained as an application. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：31 / 41

页数：11

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