Laplace-transform asymptotics of longest gaps in Poisson processes
Abstract
In a Poisson process with constant rate (also known as homogeneous Poisson process) with
exponential inter-arrival (waiting time to the next event) time, the longest/largest gap, L(t)
which is the maximal inter-arrival time is considered in this paper. The aim was to establish
the Laplace transform asymptotic and the large deviation principles related to the longest gap
L(t) between epochs of arrival in a homogeneous Poisson process. The result of the
investigation suggest two natural and different large deviation principles for the longest gap
with two distinct rate functions and speeds.
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- SIMC 2019 [99]