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The Multitype Continuous-Time Markov Branching Process in a Periodic Environment

B. Klein and P. D. M. Macdonald
Advances in Applied Probability
Vol. 12, No. 1 (Mar., 1980), pp. 81-93
DOI: 10.2307/1426495
Stable URL: http://www.jstor.org/stable/1426495
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Multitype Continuous-Time Markov Branching Process in a Periodic Environment
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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.

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