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Some generalizations of Bailey's birth death and migration model

Published online by Cambridge University Press:  01 July 2016

A. W. Davis
A. W. Davis*
Affiliation:
C.S.I.R.O., Adelaide
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Abstract

Some results for a general Markov branching-diffusion process are presented, and applied to a model recently considered by Bailey. Moments of the limiting distributions of certain natural measures of the spatial location and dispersion of the population are shown to be expressible in terms of the Lauricella FD-type hypergeometric functions, when the population multiplies according to the simple birth and death process with λ > μ.

Type
Research Article
Information
Advances in Applied Probability , Volume 2 , Issue 1 , Spring 1970 , pp. 83 - 109
Copyright
Copyright © Applied Probability Trust 

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References

Adke, S. R. and Moyal, J. E. (1963) A birth, death and diffusion process. J. Math. Anal. Appl. 7, 209–224.Google Scholar
Appell, P. and Kampe de Fertet, J. (1926) Fonctions Hypergéometriques et Hypersphériques. Gauthier Villar.Google Scholar
Bailey, N. T. J. (1968) Stochastic birth, death and migration processes for spatially distributed populations. Biometrika 55, 189–198.CrossRefGoogle Scholar
Conner, H. E. (1966) Limiting behavior for age- and position-dependent branching processes. J. Math. Anal. Appl. 13, 265–295.Google Scholar
Davis, A. W. (1965) On the theory of birth, death and diffusion processes. J. Appl. Prob. 2, 293–322.CrossRefGoogle Scholar
Davis, A. W. (1967a) Branching-diffusion processes with no absorbing boundaries. I. J. Math. Anal. Appl. 18, 276–296.Google Scholar
Davis, A. W. (1967b) Branching-diffusion processes with no absorbing boundaries. II. J. Math. Anal. Appl. 19, 1–25.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Moyal, J. E. (1962) The general theory of stochastic population processes. Acta Math. 108, 1–31.Google Scholar
Moyal, J. E. (1964) Multiplicative population processes. J. Appl. Prob. 1, 267–283.CrossRefGoogle Scholar
Sevast'yanov, B. A. (1958) Branching stochasic processes for particles diffusing in a restricted domain with absorbing boundaries. Theor. Probability Appl. 3, 111–126.Google Scholar
Watanabe, S. (1965) On the branching process for Brownian particles with an absorbing boundary. J. Math. Kyoto Univ. 4, 385–398.Google Scholar