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A multitype decomposable age-dependent branching process and its applications

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Chinsan Lee  and
Grace L. Yang
Chinsan Lee*
Affiliation:
National Sun Yat-Sen University
Grace L. Yang*
Affiliation:
University of Maryland, College Park
*
∗Postal address: Applied Mathematics Department, National Sun Yat-Sen University, Taiwan, ROC.
∗∗Postal address: Department of Mathematics, University of Maryland, College Park, MD 20742, USA.
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Abstract

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.

Keywords

COUNTING PROCESSTWO-STAGE TUMOR GROWTH MODELRENEWAL EQUATIONLIFESPAN DISTRIBUTIONASYMPTOTIC MOMENTS

MSC classification

Secondary: 60J85: Applications of branching processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 591 - 608
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research partially supported by the US EPA.

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