Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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.

Keywords

Completion time, coverage, inhomogeneous Poisson process, Johnson-Mehl model, linear birth-growth model, Markov process, strong limit theorem

Publication Date

9-2000

Source Publication Title

Advances in Applied Probability

Volume

32

Issue

3

Start Page

620

End Page

627

Publisher

Applied Probability Trust

Peer Reviewed

1

Copyright

© Applied Probability Trust 2000

Funder

Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P) and also by the National Science Foundation of China.

DOI

10.1017/S0001867800010156

Link to Publisher's Edition

https://doi.org/10.1017/S0001867800010156

ISSN (print)

00018678

ISSN (electronic)

14756064

Included in

Mathematics Commons

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