Central limit theory for the number of seeds in a growth model in Rd with inhomogeneous poisson arrivals

Sung Nok Chiu, M. P. Quine

Research output: Contribution to journalArticlepeer-review

Abstract

A Poisson point process 9 in d-dimensional Euclidean space and in time is used to generate a birth–growth model: seeds are born randomly at locations xi in Rd at times [formula]. Once a seed is born, it begins to create a cell by growing radially in all directions with speed v > 0. Points of 9 contained in such cells are discarded, that is, thinned. We study the asymptotic distribution of the number of seeds in a region, as the volume of the region tends to infinity. When d = 1, we establish conditions under which the evolution over time of the number of seeds in a region is approximated by a Wiener process. When d ≥ 1, we give conditions for asymptotic normality. Rates of convergence are given in all cases.

Original languageEnglish
Pages (from-to)802-814
JournalAnnals of Applied Probability
Volume7
Issue number3
DOIs
Publication statusPublished - Aug 1997

User-Defined Keywords

  • Birth–growth
  • inhomogeneous Poisson process
  • R d
  • central limit theorem
  • Brownian motion
  • rate of convergence

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