Department of Mathematics
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  is filled in.
Source Publication Title
Mathematical News / Mathematische Nachrichten
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.
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).
Link to Publisher's Edition
Chiu, S., & Lee, H. (2002). A regularity condition and strong limit theorems for linear birth–growth processes. Mathematical News / Mathematische Nachrichten, 241 (1), 21-27. https://doi.org/10.1002/1522-2616(200207)241:1<21::AID-MANA21>3.0.CO;2-D