TY - JOUR
T1 - A regularity condition and strong limit theorems for linear birth-growth processes
AU - Chiu, S. N.
AU - Lee, H. Y.
N1 - We thank the referees for their helpful comments. 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).
PY - 2002/7
Y1 - 2002/7
N2 - A linear birth-growth process is generated by an inhomogeneous Poisson process on IR × [0, ∞). 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 IR. 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.
AB - A linear birth-growth process is generated by an inhomogeneous Poisson process on IR × [0, ∞). 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 IR. 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.
KW - Birth-growth process
KW - Inhomogeneous Poisson process
KW - Johnson-Mehl tessellation
KW - Strong limit theorem
UR - http://www.scopus.com/inward/record.url?scp=0036065613&partnerID=8YFLogxK
U2 - 10.1002/1522-2616(200207)241:1<21::AID-MANA21>3.0.CO;2-D
DO - 10.1002/1522-2616(200207)241:1<21::AID-MANA21>3.0.CO;2-D
M3 - Journal article
AN - SCOPUS:0036065613
SN - 0025-584X
VL - 241
SP - 21
EP - 27
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 1
ER -