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On a probabilistic analogue of the Fibonacci sequence

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
*
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 1965, Canberra City, A.C.T. 2601, Australia.
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Abstract

One of the earliest population models to be studied gives rise to the Fibonacci sequence and has a history dating back more than 750 years. A stochastic version of the model is discussed in this paper, its basic defining property being E(Xn | Xn−1, · ··, X0) = Xn−1 + Xn−2 a.s. The process {Xn} mimics many of the standard properties of the Fibonacci sequence. In particular, under mild additional conditions, a.s. as n → where α is the ‘golden ratio'

Keywords

POPULATION PROCESSESGROWTH RATESFIBONACCI NUMBERSGOLDEN RATIOGENERALIZED MARTINGALES
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1079 - 1082
Copyright
Copyright © Applied Probability Trust 

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References

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