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LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES

Part of: Integral transforms, operational calculus Stochastic processes Limit theorems

Published online by Cambridge University Press:  16 October 2019

JOSEPH OKELLO OMWONYLEE Open the ORCID record for JOSEPH OKELLO OMWONYLEE [Opens in a new window]
JOSEPH OKELLO OMWONYLEE*
Affiliation:
Department of Mathematics, Makerere University, Kampala, Uganda email jokello@kyu.ac.ug
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Abstract

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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 $t\rightarrow \infty$ and derive two natural and different large-deviation principles for $L(t)$ with two distinct rate functions and speeds.

Keywords

longest gapLaplace transformlarge-deviation principlePoisson process

MSC classification

Primary: 60F10: Large deviations
Secondary: 44A10: Laplace transform 60G50: Sums of independent random variables; random walks 60G70: Extreme value theory; extremal processes

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 146 - 156
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

We acknowledge financial support extended from the Sida bilateral program with Makerere University, phase IV 2015–2020, project 316, Capacity Building in Mathematics and Its Applications.

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