The time of completion of a linear birth-growth model

Sung Nok CHIU*, C. C. Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Consider the following birth-growth model in R. Seeds are born randomly according to an inhomogeneous space-time Poisson process. A newly formed point immediately initiates a bi-directional coverage by sending out a growing branch. Each frontier of a branch moves at a constant speed until it meets an opposing one. New seeds continue to form on the uncovered parts on the line. We are interested in the time until a bounded interval is completely covered. The exact and limiting distributions as the length of interval tends to infinity are obtained for this completion time by considering a related Markov process. Moreover, some strong limit results are also established.

Original languageEnglish
Pages (from-to)620-627
Number of pages8
JournalAdvances in Applied Probability
Volume32
Issue number3
DOIs
Publication statusPublished - 2000

Scopus Subject Areas

  • Statistics and Probability
  • Applied Mathematics

User-Defined Keywords

  • Completion time
  • Coverage
  • Inhomogeneous poisson process
  • Johnson-Mehl model
  • Linear birth-growth model
  • Markov process
  • Strong limit theorem

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