Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

A linear birth-growth process is generated by an inhomogeneous Poisson process on R x [0, infinity). Seeds are born randomly according to the Poisson process. Once a seed is born, it commences immediately to grow bidirectionally with a constant speed. The positions occupied by growing intervals are regarded as covered. New seeds continue to form on the uncovered part of R. This paper shows that the total number of seeds born on a very long interval satisfies the strong invariance principle and some other strong limit theorems. Also, a gap (an unproved regularity condition) in the proof of the central limit theory in [5] is filled in.

Publication Date

7-2002

Source Publication Title

Mathematical News / Mathematische Nachrichten

Volume

241

Issue

1

Start Page

21

End Page

27

Publisher

Wiley-VCH Verlag

Peer Reviewed

1

Copyright

This is the peer reviewed version of the following article: Chiu, S. N. and Lee, H. Y. (2002), A Regularity Condition and Strong Limit Theorems for Linear Birth–Growth Processes. Math. Nachr., 241: 21–27. doi:10.1002/1522-2616(200207)241:1<21::AID-MANA21>3.0.CO;2-D, which has been published in final form at http://dx.doi.org/10.1002/1522-2616(200207)241:1%3C21::AID-MANA21%3E3.0.CO;2-D. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Funder

The first author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P).

DOI

10.1002/1522-2616(200207)241:1<21::AID-MANA21>3.0.CO;2-D

ISSN (print)

0025584X

ISSN (electronic)

15222616

Included in

Mathematics Commons

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