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

Mehri Javanian; Mohammad Q. Vahidi-Asl

doi:10.2478/v10294-012-0015-1

.blurhash-client-img { display: none !important; }

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

Journal of Applied Mathematics, Statistics and Informatics

Volume 8 (2012): Issue 2 (December 2012)

By: Mehri Javanian and Mohammad Q. Vahidi-Asl

Open Access

|Apr 2013

Abstract

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

References

D. Y. C. Chan, B. D. Hughes, A. S. Leong, W. J. Reed, Stochasticaly evolving networks, Phys. Rev. E, 68 (2003), 24.10.1103/PhysRevE.68.066124
Search in Google Scholar
B. Chauvin, T. Klein, J. Marckert, A. Rouault, Martingales and Profile of Binary Search Trees. Electronic Journal of Probability, 10 (2005), 420-435.
Search in Google Scholar
R. Dobrow, and R. Smythe, Poisson approximations for functionals of random trees. Random Structures Algorithms, 9 (1996), 79-92.10.1002/(SICI)1098-2418(199608/09)9:1/2<;79::AID-RSA5>3.0.CO;2-8
Search in Google Scholar
Q. Feng, C. Su, The structure and distances in Yule recursive trees Random Struct. Algorithms, 31 (2007), 273-287.10.1002/rsa.20183
Search in Google Scholar
J. L. Gastwirth, P. K. Bhattacharya, Two probability models of pyramids or chain letter schemes demonstrating that their promotional claims are unreliable. Operations Research, 32 (1984), 527-536.
Search in Google Scholar
H. Mahmoud, R. T. Smythe, A survey of recursive trees, Theory Probab. Math. Statist., 51 (1995), 1-27.
Search in Google Scholar
S. M. Ross, Stochastic processes, Wiley, New York, 1983.10.1016/B978-0-12-598420-1.50011-8
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10294-012-0015-1 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180

Journal RSS Feed

Language: English

Page range: 67 - 72

Published on: Apr 13, 2013

Published by: University of Ss. Cyril and Methodius in Trnava

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Yule processes,

recursive trees

Related subjects:

Computer sciences,

Information technology,

Mathematics,

Logic and set theory,

Probability and statistics,

Applied mathematics

© 2013 Mehri Javanian, Mohammad Q. Vahidi-Asl, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons License.

Volume 8 (2012): Issue 2 (December 2012)