Functional limit theorems for Levy processes satisfying Cramer's condition

被引：4

作者：

Barczy, Matyas ^{[1
]}

Bertoin, Jean ^{[2
]}

机构：

[1] Univ Debrecen, Dept Appl Math & Probabil, Fac Informat, H-4010 Debrecen, Hungary

[2] UPMC, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2011年 / 16卷

基金：

匈牙利科学研究基金会;

关键词：

Levy process; Cramer's condition; self-similar Markov process; RECURRENT EXTENSIONS;

D O I：

10.1214/EJP.v16-930

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 consider a Levy process that starts from x < 0 and conditioned on having a positive maximum. When Cramer's condition holds, we provide two weak limit theorems as x -> -infinity for the law of the (two-sided) path shifted at the first instant when it enters (0, infinity), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes

引用

页码：2020 / 2038

页数：19

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