A non-Markovian model for cell population growth: speed of convergence and central limit theorem

Mathisca C. M. de Gunst and Willem R. van Zwet

Stochastic Processes and their Applications, 1992, vol. 41, issue 2, 297-324

Abstract: In De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour 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 theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data.

Keywords: stochastic; model; population; growth; non-Markovian; counting; process; almost; sure; converegence; rate; of; convergence; central; limit; theorem (search for similar items in EconPapers)
Date: 1992
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