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The expected population size in a cell-size-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
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Abstract

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

Keywords

CELL-SIZE-DEPENDENTBRANCHING PROCESSBIRTH-AND-DEATH PROCESSINTEGRAL OPERATORS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 65 - 75
Copyright
Copyright © Applied Probability Trust 

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References

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