IJPAM: Volume 45, No. 2 (2008)

BRANCHING PROCESSES WITH
A COMMON EXTINCTION PROBABILITY

Myron Hlynka$^1$, Wayne Horn$^2$, Richard Schell$^3$
$^{1,3}$Department of Mathematics and Statistics
University of Windsor
Windsor, Ontario, N9B 3P4, CANADA
$^1$e-mail: hlynka@uwindsor.ca
$^3$e-mail: rick_schell@gecdsb.on
$^2$Department of Mathematics and Statistics
Carleton University
Ottawa, Ontario, K1S 5B6, CANADA
e-mail: whorn@math.carleton.ca


Abstract.We present a method of creating a class of branching processes with a common probability of extinction. For our specialized setting, one member of the class involves probabilities that involve Fibonacci numbers. By using another method to obtain the probabilities, we obtain a new expression for the $n$-th Fibonacci number.

Received: February 3, 2008

AMS Subject Classification: 60J80, 05A10, 11K31

Key Words and Phrases: branching, Fibonacci numbers, double sided ballot theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 2