Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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.

Keywords

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

Publication Date

8-1997

Source Publication Title

Annals of Applied Probability

Volume

7

Issue

3

Start Page

802

End Page

814

Publisher

Institute of Mathematical Statistics

Peer Reviewed

1

Funder

Research partially supported by an Australian Research Council Institutional Grant.

DOI

10.1214/aoap/1034801254

Link to Publisher's Edition

https://dx.doi.org/10.1214/aoap/1034801254

ISSN (print)

10505164

Included in

Mathematics Commons

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