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The time of completion of a linear birth-growth model

Published online by Cambridge University Press:  19 February 2016

S. N. Chiu*
Affiliation:
Hong Kong Baptist University
C. C. Yin*
Affiliation:
Hong Kong Baptist University and Qufu Normal University
*
Postal address: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
∗∗ Email address: [email protected]

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.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

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 Natural Science Foundation of China.

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