Non-Markovian Model for Cell Population Growth; Asymptotic Properties 1: Speed of Convergence and Central Limit Theorem

摘要

In De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In the paper the mathematical properties of the model are considered. The authors investigate the asymptotic behavior of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular, it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theroem is proved. Computer simulations illustrate the behavior of the process. The model is graphically compared with experimental data.