A new characterisation property of mixed poisson processes via Berman's theorem

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Abstract

In the literature on mixed Poisson processes, a number of characterisation properties have been studied. As a new characterisation property for mixed Poisson processes, we show that normalised event occurrence times are the order statistics of independent uniform random variables on (0, 1). Berman's theorem on lp-isotropic sequences is applied to prove the results.

Original languageEnglish
Pages (from-to)261-268
Number of pages8
JournalJournal of Applied Probability
Volume37
Issue number1
Publication statusPublished - 2000 Mar
Externally publishedYes

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Keywords

  • Berman's theorem
  • Exchangeability
  • L-isotropy
  • Mixed Poisson processes

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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