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Limit theorems for a general critical branching process

Published online by Cambridge University Press:  14 July 2016

Stephen D. Durham
Stephen D. Durham*
Affiliation:
University of Colorado
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Extract

A general branching process begins with an initial object born at time 0. The initial object lives a random length of time and, during its life-time, has offspring which reproduce and die as independent probabilistic copies of the parent. Number and times of births to a parent are random and, once an object is born, its behavior is assumed to be independent of all other objects, independent of total population size and independent of absolute time. The life span of a parent and the number and times its offspring arrive may be interdependent. Multiple births are allowed. The process continues as long as there are objects alive.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 1 - 16
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Chover, J. and Ney, P. (1968) The non-linear renewal equation. J. Analyse Math. 21, 381–413.Google Scholar
[2] Crump, K. and Mode, C. (1968) A general age-dependent branching process. J. Math. Anal. Appl. 24, 494–508.Google Scholar
[3] Crump, K. and Mode, C. (1969) A general age-dependent branching process. II. J. Math. Anal. Appl. 25, 8–17.CrossRefGoogle Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and Its Applications Volume II. Wiley, New York.Google Scholar
[5] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[6] Ryan, T. A. Jr. (1968) On Age-dependent Branching Processes. Ph.D. Dissertation, Cornell University. [Unpublished].Google Scholar
[7] Sevast'Yanov, B. A. (1964) Age-dependent branching process. Theor. Prob. Appl. 9, 577–594.Google Scholar
[8] Sevast'Yanov, B. A. (1967) Asymptotic behavior of the probability of non-extinction of a critical brahching process. Theor. Prob. Appl. 12, 152–154.Google Scholar
[9] Weiner, H. J. (1965) Asymptotic properties of an age-dependent branching process. Ann. Math. Statist. 36, 1565–1568.Google Scholar