Article contents
The multitype continuous-time Markov branching process in a periodic environment
Published online by Cambridge University Press: 01 July 2016
Abstract
The multitype continuous-time Markov branching process has many biological applications where the environmental factors vary in a periodic manner. Circadian or diurnal rhythms in cell kinetics are an important example. It is shown that in the supercritical positively regular case the proportions of individuals of various types converge in probability to a non-random periodic vector, independent of the initial conditions, while the absolute numbers of individuals of various types converge in probability to that vector multiplied by a random variable whose distribution depends on the initial conditions. It is noted that the proofs are straightforward extensions of the well-known results for a constant environment.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Applied Probability Trust 1980
Footnotes
Financial support from INSERM contract #77-5-049-2 and from the National Research Council of Canada is acknowledged.
References
- 13
- Cited by