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.
Original language | English |
---|---|
Pages (from-to) | 620-627 |
Number of pages | 8 |
Journal | Advances in Applied Probability |
Volume | 32 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2000 |
Scopus Subject Areas
- Statistics and Probability
- Applied Mathematics
User-Defined Keywords
- Completion time
- Coverage
- Inhomogeneous poisson process
- Johnson-Mehl model
- Linear birth-growth model
- Markov process
- Strong limit theorem