LIMITING PROBABILITY TRANSITION MATRIX
OF A CONDENSED FIBONACCI TREE
K.A. Germina
Department of Mathematics
Central University of Kerala
Kasargod, Kerala, INDIA

Abstract

This paper discusses on the construction of condensed Fibonacci trees and present the Markov chain corresponding to the condensed Fibonacci trees. An $n \times n$ finite Markov probability transition matrix for this Markov chain is presented and it is proved that the limiting steady state probabilities are proportional to the first $n$ Fibonacci numbers.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 2
Year: 2018

DOI: 10.12732/ijam.v31i2.6

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] X. Cao, J. Zhang, Event-based optimization of Markov systems, IEEE Trans Automatic Control, 53, No 4 (2008), 1076–1082.
  2. [2] Y. Horibe, An entropy view of Fibonacci trees, The Fibonacci Quarterly, 20, No 2 (1982), 168–178.
  3. [3] F. Spitzer, Principles of Random Walk, Springer, New York (1964).