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The point-process approach to age- and time-dependent branching processes

Published online by Cambridge University Press:  01 July 2016

Marek Kimmel
Marek Kimmel*
Affiliation:
Silesian Technical University
*
∗Postal address: Institute of Automation, Silesian Technical University, 44–100 Gliwice, Pstrowskiego 16, Poland.
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Abstract

The multitype age-dependent branching process in varying environment is treated as a random stream (point process) of the birth and death events. We derive the point-process version of the Bellman–Harris equation, which provides us with a symbolic method of writing the equations for the arbitrary finite-dimensional distribution of the process. We also derive a new recurrence relation, the ‘principle of last generation'. This result is applied to obtain new moment equations for the process with immigration also. General considerations are illustrated by a simple cell kinetics model.

Keywords

VARYING ENVIRONMENTIMMIGRATIONPROBABILITY GENERATING FUNCTIONALFUNCTIONAL EQUATIONSYMBOLIC METHODPRINCIPLE OF LAST GENERATIONMOMENT EQUATIONSCANCER CELL CYCLE
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 1 - 20
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This work was supported in part by the Polish Academy of Sciences grant No. 10.4.3.01.4.

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