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Journal of Applied Mathematics, Statistics and Informatics

The Journal of University of Saint Cyril and Metodius

Editor-in-Chief: Kvasnicka, Vladimír

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A Strong Law for the Size of Yule M-Oriented Recursive Trees

Mehri Javanian / Mohammad Q. Vahidi-Asl
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  • Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran
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Published Online: 2013-04-13 | DOI: https://doi.org/10.2478/v10294-012-0015-1


Let Nt be the total number of nodes in a Yule m-oriented recursive tree at time t. Then {Nt : t ∈ [0;1)} is a Yule process with birth rates λn = (m(n - 1) + 1)λ for n ≥ 1, where N0 = 1. In this paper, we first give the exact distribution of Nt, then prove that

, almost surely

Additional Key Words and Phrases: Yule processes; recursive trees

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About the article

Published Online: 2013-04-13

Published in Print: 2012-12-01

Citation Information: Journal of Applied Mathematics, Statistics and Informatics, Volume 8, Issue 2, Pages 67–72, ISSN (Print) 1336-9180, DOI: https://doi.org/10.2478/v10294-012-0015-1.

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