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Multiplicative population processes

Published online by Cambridge University Press:  14 July 2016

J. E. Moyal
J. E. Moyal*
Affiliation:
Argonne National Laboratory, Argonne, Illinois
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Extract

The theory of multiplicative (or branching) population processes where the states of each individual in the population range over a fixed finite set has been studied by a number of authors: see for example, Everett and Ulam, Kolmogorov and Sevastyanov, Harris; the continuous parameter case is treated in Arley; further references will be found in the books by Bartlett and Bharucha-Reid. The purpose of the present paper is to study the theory of such processes in the case where the individual state space is arbitrary (i.e., an abstract space).

Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 267 - 283
Copyright
Copyright © Applied Probability Trust 

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References

[1] Arley, N. (1948) On the Theory of Stochastic Processes and their Applications to the Theory of the Cosmic Radiation. John Wiley, New York.Google Scholar
[2] Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge U. P. Google Scholar
[3] Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and Their Applications. McGraw Hill, New York.Google Scholar
[4] Everett, C. J. and Ulam, S. (1948) Multiplicative systems in several variables. I, II and III. Los Alamos Scientific Laboratory Declassified Documents, LADC - 533, 534, LA - 707.Google Scholar
[5] Harris, T. E. (1951) Some mathematical models for branching processes. Proc. 2nd Berkeley Symposium on Math. Statistics and Probability, 305–328.Google Scholar
[6] Kolmogorov, A. N. and Sevastyanov, B. A. (1947) The calculation of final probabilities for branching stochastic processes. Dokl. Akad. Nauk, S.S.S.R. 59, 783–786.Google Scholar
[7] Moyal, J. E. (1957) Discontinuous Markoff processes. Acta Math. Stockh. 98, 221–264.Google Scholar
[8] Moyal, J. E. (1962) The general theory of stochastic population processes. Acta Math., Stockh. 108, 1–31.CrossRefGoogle Scholar
[9] Moyal, J. E. (1962) Multiplicative population chains. Proc. Roy. Soc. A 266, 518–526.Google Scholar