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Diffusion limits of critical branching processes conditioned on extinction in the near future

Published online by Cambridge University Press:  14 July 2016

Warren W. Esty*
Affiliation:
Cleveland State University
*
*Now at Montana State University, Bozeman, Montana.

Abstract

Limit laws and limiting diffusions are obtained for critical branching processes, either Galton-Watson or age-dependent, conditioned on extinction in the interval (T, cT], 1 < c, as T→∞, and also as T→∞ and c ↓ 1.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Heidelberg.Google Scholar
[2] Esty, W. W. (1975) Critical age-dependent branching processes. Ann. Prob. 3, 4960.Google Scholar
[3] Esty, W. W. (1975) Critical age-dependent branching process diffusions. Stoch. Proc. Appl. To appear.CrossRefGoogle Scholar
[4] Esty, W. W. (1975) The reverse Galton-Watson process. J. Appl. Prob. 12, 574580.Google Scholar
[5] Gikhman, I. I. and Skorokhod, A. V. (1969) Introduction to the Theory of Random Processes. W. B. Saunders Co., Philadelphia.Google Scholar