Cumulative record times in a Poisson process

Details Cumulative record times in a Poisson process Cumulative record times in a Poisson process

2007-12-20

arxiv.org/abs/0712.3420v1

Mathematics

Probability

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.i

Scientific paper

We obtain a strong law of large numbers and a functional central limit
theorem, as $t\to\infty$, 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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