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LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 16 October 2019, pp. 146-156
- Print publication:
- February 2020
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- Article
- Export citation
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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.
