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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 80, 2008 - Issue 2-3: A Festschrift for Priscilla Greenwood
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Original Articles

Cumulative record times in a Poisson process

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Pages 157-174 | Received 13 Sep 2007, Accepted 01 Nov 2007, Published online: 09 Oct 2008
 

Abstract

We obtain a strong law of large numbers and a functional central limit theorem, as t → ∞, for the number of records up to time t and the Lebesgue measure (length) of the subset of the time interval [0, t] during which the Poisson process is in a record lifetime.

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