On some tractable growth-collapse processes with renewal collapse EPOCHS

Onno Boxma, Offer Kella, David Perry

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we generalize existing results for the steady-state distribution of growthcollapse processes with independent exponential intercollapse times to the case where they have a general distribution on the positive real line having a finite mean. In order to compute the moments of the stationary distribution, no further assumptions are needed. However, in order to compute the stationary distribution, the price that we are required to pay is the restriction of the collapse ratio distribution from a general distribution concentrated on the unit interval to minus-log-phase-type distributions. A random variable has such a distribution if the negative of its natural logarithm has a phase-type distribution. Thus, this family of distributions is dense in the family of all distributions concentrated on the unit interval. The approach is to first study a certain Markovmodulated shot noise process from which the steady-state distribution for the related growth-collapse model can be inferred via level crossing arguments.

Original languageEnglish
Pages (from-to)217-234
Number of pages18
JournalJournal of Applied Probability
Volume48 A
DOIs
StatePublished - 2011

Keywords

  • Growth collapse
  • Markov modulated
  • Minus-log-phase-type distribution
  • Shot noise process

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

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