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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Branching processes in simple random walk


Author: Meyer Dwass
Journal: Proc. Amer. Math. Soc. 51 (1975), 270-274
MSC: Primary 60J15; Secondary 60J80
DOI: https://doi.org/10.1090/S0002-9939-1975-0370775-4
MathSciNet review: 0370775
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ N(a)$ be the number of overcrossings of height $ a$ in a simple random walk. For $ p < 1/2$, the process $ N(0),N(1), \ldots $ is a branching process which eventually becomes extinct. For $ 1/2 < p,N(0),N(1), \ldots $ is a stationary process which is a branching process with immigration.


References [Enhancements On Off] (What's this?)

  • [1] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0370775-4
Keywords: Branching process, branching process with immigration, random walk, simple random walk
Article copyright: © Copyright 1975 American Mathematical Society