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A stochastic population projection system based on general age-dependent branching processes

Published online by Cambridge University Press:  14 July 2016

Charles J. Mode ,
Marc E. Jacobson  and
Gary T. Pickens
Charles J. Mode*
Affiliation:
Drexel University
Marc E. Jacobson*
Affiliation:
University of Pennsylvania
Gary T. Pickens*
Affiliation:
Drexel University
*
∗Postal address: Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA 19104, USA.
∗∗Postal address: Department of Statistics, University of Pennsylvania, Philadelphia, PA 19104, USA.
∗Postal address: Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA 19104, USA.
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Abstract

Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the process as well as variances and covariances, measuring variation about means. Four exploratory population projections, testing the implications of the algorithms for the case of time-homogeneous laws of evolution, are presented. Formulas extending mean and variance functions for unit population projections to an arbitrary initial population size are also presented. These formulas show that, in population processes with non-random laws of evolution, stochastic fluctuations about the mean function are negligible when initial population size is large. Further extensions of these formulas to the case of randomized laws of evolution suggest that stochastic fluctuations about the mean function can be significant even for large initial populations.

Keywords

STOCHASTIC POPULATION PROCESSESALGORITHMSDISCRETE TIMEBIRTH COHORTSLESLIE MATRIXVARIANCE AND COVARIANCE FUNCTIONSUNIT POPULATION PROJECTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 1 - 13
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

†

Supported in part by NICHD Grant R01 HD 09571.

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