A GENERAL STOCHASTIC MODEL FOR NUCLEATION AND LINEAR GROWTH
成果类型：
Article
署名作者：
Holst, L.; Quine, M. P.; Robinson, J.
署名单位：
Royal Institute of Technology; University of Sydney
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
903-921
关键词：
摘要：
The model considered here has arisen in a number of completely separate contexts: release of neurotransmitter at neuromuscular synapses, unravelling of strands of DNA, differentiation of cells into heterocysts in algae and growth of crystals. After a shear transformation the model becomes a Markov process, based on a Poisson process on the upper half plane, homogeneous in the horizontal (time) direction, which increases at unit rate except for occasional drops. By considering the process separately when it is above or below a given level,for any interval on the time axis, we obtain in particular exact moment results and prove asymptotic normality for long time intervals for the number of downcrossings in the interval, the total time in the interval when the process is below the specified level and the number of drops in the interval. Limit distributions as the length of interval tends to in finity are obtained for the level at which the interval is covered. It is shown that several problems considered in the literature have analytic solutions as special cases of the general model. The numerical results from one special case are compared to statistics obtained from experimental data from neurobiology.