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Moments for a general branching process in a semi-Markovian environment

Published online by Cambridge University Press:  14 July 2016

Craig Whittaker  and
Richard M. Feldman
Craig Whittaker*
Affiliation:
Texas A&M University
Richard M. Feldman*
Affiliation:
Texas A&M University
*
∗Postal address: Department of Industrial Engineering, Biosystems Research Division, Texas A&M University, College Station, TX 77843, U.S.A.
∗Postal address: Department of Industrial Engineering, Biosystems Research Division, Texas A&M University, College Station, TX 77843, U.S.A.
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Abstract

A general branching process is extended to allow life length and reproduction probabilities to depend on randomly changing environmental states. First and second moments of the population size with respect to time are derived assuming that the environmental process is semi-Markovian. The results are similar to Markov-renewal type equations which allow, under discrete time, iterative computation of both moments of the population through time.

Keywords

GENERAL BRANCHING PROCESSMARKOV RENEWALSEMI-MARKOV
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 341 - 349
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

This work was funded in part by a U.S. Department of Agriculture sponsored program entitled ‘The Expanded Southern Pine Beetle Research and Applications Program' Grant Number 89–106 (19–258) and in part by the National Science Foundation and the Environmental Protection Agency, through a Grant (NSF GB-34718) to the University of California.

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