LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES

被引：1

作者：

Omwonylee, Joseph Okello ^{[1
]}

机构：

[1] Makerere Univ, Dept Math, Kampala, Uganda

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 101卷 / 01期

关键词：

longest gap; Laplace transform; large-deviation principle; Poisson process; RUNS; LAW;

D O I：

10.1017/S0004972719000972

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The longest gap L(t) up to time t in a homogeneous Poisson process is the maximal time subinterval between epochs of arrival times up to time t; it has applications in the theory of reliability. We study the Laplace transform asymptotics for L(t) as t ! 1 and derive two natural and di fferent large-deviation principles for L(t) with two distinct rate functions and speeds.

引用

页码：146 / 156

页数：11

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