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.
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页码：146 / 156
页数：11
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