A new proof of Yaglom’s exponential limit law

Geiger, Jochen

doi:10.1007/978-3-0348-8405-1_21

Jochen Geiger³

Part of the book series: Trends in Mathematics ((TM))

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Abstract

Let (Z_n)_n≥0 be a critical Galton-Watson branching process with finite variance. We give a new proof of a classical result by Yaglom that Z _n conditioned on Zn > 0 has an exponential lirnit law.

Research supported by Deutsche Forschungsgemeinschaft

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References

Athreya, K. B. and Ney, P. (1972) Branching Processes, Springer, New York.
Book MATH Google Scholar
Bickel, P. J. and Freedman, D. A. (1981) Some asymptotic theory for the bootstrap, Ann. Statist. 9, 1196–1217.
Article MathSciNet MATH Google Scholar
Fleischmann, K. and Siegmund-Schultze, R. (1977) The structure of reduced critical Galton-Watson processes, Math. Nachr. 79, 233–241.
Article MathSciNet Google Scholar
Geiger, J. (1999) Elementary new proofs of classical limit theorems for GaltonWatson processes, J. Appl. Prob. 36, 301–309.
Article MathSciNet MATH Google Scholar
Kesten, H., Ney, P. and Spitzer, F. (1966) The Galton-Watson process with mean one and finite variance, Theory Prob. Appl. 11, 513–540.
Article MathSciNet Google Scholar
Kotz, S. and Steutel, F. W. (1988) Note on a characterization of exponential distributions, Stat. Prob. Lett. 6, 201–203.
Article MathSciNet MATH Google Scholar
Liu, Q. (1998) Fixed points of a generalized smoothing transformation and applications to the branching random walk, Adv. Appl. Prob. 30, 85–112.
Article MATH Google Scholar
Lyons, R., Pemantle, R. and Peres, Y. (1995) Conceptual proofs of L log L criteria for mean behavior of branching processes, Ann. Prob. 25, 1125–1138.
Article MathSciNet Google Scholar
Rachev, S. T. and Rüschendorf, L. (1995) Probability metrics and recursive algorithms, Adv. Appl. Prob. 27, 770–799.
Article MATH Google Scholar
Rösler, U. (1991) A limit theorem for ”Quicksort”, Inform. Theor. Appl. 25, 85–100.
MATH Google Scholar
Rösler, U. (1992) A fixed point theorem for distributions, Stoch. Proc. Appl. 37, 195–214.
Article Google Scholar
Yaglom, A. M. (1947) Certain limit theorems of the theory of branching processes, Dokl. Acad. Nauk. SSSR 56, 795–798.
MathSciNet MATH Google Scholar

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Fachbereich Mathematik, Universität Frankfurt, 11 19 32, D-60054, Frankfurt, Germany
Jochen Geiger

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Jochen Geiger
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Editors and Affiliations

Bâtiment Descartes, Université de Versailles-St-Quentin PRISM, 45 avenue des Etats-Unis, 78035, Versailles, Cedex, France
Danièle Gardy
Département de Mathématiques Bâtiment Fermat, Université de Versailles-St-Quentin, 45 avenue des Etats-Unis, 78035, Versailles, Cedex, France
Abdelkader Mokkadem

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Geiger, J. (2000). A new proof of Yaglom’s exponential limit law. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_21

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DOI: https://doi.org/10.1007/978-3-0348-8405-1_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9553-8
Online ISBN: 978-3-0348-8405-1
eBook Packages: Springer Book Archive

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