Large deviations for renewal processes

被引：32

作者：

Lefevere, Raphael ^{[2
]}

Mariani, Mauro ^{[3
]}

Zambotti, Lorenzo ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, CNRS, UMR 7599,UFR Math, F-75252 Paris 05, France

[2] Univ Paris 07, Lab Probabil & Modeles Aleatoires, CNRS, UMR 7599,UFR Math, F-75205 Paris 13, France

[3] Univ Aix Marseille, Lab Anal, CNRS, Fac Sci & Tech St Jerome,UMR 6632, F-13397 Marseille 20, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2011年 / 121卷 / 10期

关键词：

Large deviations; Renewal process; Cumulative process; Heavy tails;

D O I：

10.1016/j.spa.2011.06.005

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 investigate large deviations for the empirical measure of the forward and backward recurrence time processes associated with a classical renewal process with arbitrary waiting-time distribution. The Donsker-Varadhan theory cannot be applied in this case, and indeed it turns out that the large deviations rate functional differs from the one suggested by such a theory. In particular, a non-strictly convex and non-analytic rate functional is obtained. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2243 / 2271

页数：29

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