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Branching processes and functional differential equations determining steady-size distributions in cell populations

Part of: Markov processes Mathematical biology in general

Published online by Cambridge University Press:  14 July 2016

Ziad Taib
Ziad Taib*
Affiliation:
Chalmers University of Technology and the University of Göteborg
*
∗ Postal address: Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S-412 96 Göteborg, Sweden.
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Abstract

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

Keywords

MULTITYPE BRANCHING PROCESSPOPULATION MODELS

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 92B05: General biology and biomathematics 92D25: Population dynamics (general)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 1 - 10
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by the Swedish Institute.

References

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