Cumulative record times in a Poisson process

Charles M. Goldie; Rudolf Grübel

Cumulative record times in a Poisson process

Probability 2008-01-03 v1

Authors: Charles M. Goldie , Rudolf Grübel

Abstract

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.

Keywords

poisson processes

Cite

@article{arxiv.0712.3420,
  title  = {Cumulative record times in a Poisson process},
  author = {Charles M. Goldie and Rudolf Grübel},
  journal= {arXiv preprint arXiv:0712.3420},
  year   = {2008}
}

Comments

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)

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