Department of Mathematics
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.
Completion time, coverage, inhomogeneous Poisson process, Johnson-Mehl model, linear birth-growth model, Markov process, strong limit theorem
Source Publication Title
Advances in Applied Probability
Applied Probability Trust
© Applied Probability Trust 2000
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.
Link to Publisher's Edition
Chiu, S. (2000). The time of completion of a linear birth-growth model. Advances in Applied Probability, 32 (3), 620-627. https://doi.org/10.1017/S0001867800010156