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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Branching processes in simple random walk
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by Meyer Dwass PDF
Proc. Amer. Math. Soc. 51 (1975), 270-274 Request permission

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
  • William Feller, An introduction to probability theory and its applications. Vol. I, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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