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Abstract: . We give complete proofs of the theorem of convergence of types and the Kesten-Stigum theorem for multi-type branching processes. Very little analysis is used beyond the strong law of large numbers and some basic measure theory. AMS(MOS) subject classifications. Primary 60J80. Key words and phrases. Galton-Watson, size-biased distribution. Consider a multi-type Galton-Watson branching process with J types. Let L (i;j) be a random variable representing the number of particles of type j... (Update)
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BibTeX entry: (Update)
Kurtz,T., Lyons,R., Pemantle,R. and Peres,Y.(1997): A conceptual proof of Kesten-Stigum theorem for multi-type branching processes, Classical and Modern Branching Processes, 181-186, IMA Volumes in Mathematics and its Applications, Vol. 84, Springer, New York. http://citeseer.ist.psu.edu/kurtz97conceptual.html More
@misc{ kurtz97conceptual,
author = "T. Kurtz and R. Lyons and R. Pemantle and Y. Peres",
title = "A conceptual proof of Kesten-Stigum theorem for multi-type branching processes",
text = "Kurtz,T., Lyons,R., Pemantle,R. and Peres,Y.(1997): A conceptual proof
of Kesten-Stigum theorem for multi-type branching processes, Classical and
Modern Branching Processes, 181-186, IMA Volumes in Mathematics and its
Applications, Vol. 84, Springer, New York.",
year = "1997",
url = "citeseer.ist.psu.edu/kurtz97conceptual.html" }
Citations (may not include all citations):196 Probability: Theory and Examples (context) - Durrett - 1991
116 Branching Processes - Athreya, Ney - 1972
10 A limit theorem for multidimensional GaltonWatson processes (context) - Kesten, Stigum - 1966
8 Conceptual proofs of L log L criteria for mean behavior of b.. - Lyons, Pemantle et al. - 1995
2 Almost sure convergence of the type distribution for a super.. (context) - Kurtz - 1973
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