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Galton-Watson processes in varying environments

Published online by Cambridge University Press:  14 July 2016

Peter Jagers
Peter Jagers*
Affiliation:
Gothenburg University, Sweden
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Abstract

Galton-Watson processes where the reproduction of individuals in different generations can have different distributions retain many characteristic features of classical processes.

Keywords

GALTON-WATSON BRANCHING PROCESSRANDOM ENVIRONMENTDIFFUSION APPROXIMATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 174 - 178
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Athreya, K. B. and Karlin, S. (1971) On branching processes with random environments. I and II. Ann. Math. Statist. 42, 1499–1520 and 1843–1858.CrossRefGoogle Scholar
[2] Chung, K. L. (1968) A Course in Probability Theory. Harcourt, Brace and World, New York.Google Scholar
[3] Church, J. D. Composition limit theorems for probability generating functions. MRC Techn. Summ. Rept. No. 732, Math. Res. Center, Madison, Wisconsin.Google Scholar
[4] Fahady, K. S., Quine, M. P. and Vere-Jones, D. (1971) Heavy traffic approximations for the Galton-Watson process Adv. Appl. Prob. 3, 282–300.CrossRefGoogle Scholar
[5] Feller, W. (1951) Diffusion processes in genetics. Proc. Second Berkeley Symp. Math. Statist. Prob. 227–246. Univ. of California Press.Google Scholar
[6] Jiřina, M. (1969) On Feller's branching diffusion processes Casopis Pest. Mat. 94, 84–90.CrossRefGoogle Scholar
[7] Kaplan, N. (1972) A theorem on composition of random probability generating functions and applications to branching processes with random environments J. Appl. Prob. 9, 1–12.CrossRefGoogle Scholar
[8] Nagayev, S. V. and Muhamedhanova, R. (1966) Perehodnyie yavleniya v vetvyašcihsya slucaynyh protsessah s diskretnym vremenem. Predelnyie teoremy i statisticeskiye vyvody, Tashkent. (Correction to this in 1968, same publication.) Google Scholar
[9] Sevast'Yanov, B. A. (1971) Vetvyašciesya protsessy. Mir, Moscow.Google Scholar
[10] Smith, W. L. and Wilkinson, W. E. (1969) On branching processes in random environments Ann. Math. Statist. 40, 814–827.CrossRefGoogle Scholar
[11] Seneta, E. (1970) Population growth and the multitype Galton-Watson process Nature 225, 766.CrossRefGoogle ScholarPubMed