On suprema of Levy processes with light tails

被引：2

作者：

Braverman, Michael ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 04期

关键词：

Poisson process; Brownian motion; Supremum; COMPOUND POISSON; APPROXIMATIONS; FUNCTIONALS;

D O I：

10.1016/j.spa.2009.12.004

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：

Let X(t), t >= 0, X(0) = 0, be a Levy process with a spectral Levy measure rho. Assuming that integral(1)(-1)vertical bar x vertical bar rho(dx) < infinity and the right tail of rho is light, we show that in the presence of the Brownian component P((sup)(0 <= t <= 1) X(t) > u) similar to P (X(1) > u) as u -> infinity, while in the absence of a Brownian component these tails are not always comparable. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：541 / 573

页数：33

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