A note on Fibonacci Sequences of Random Variables
Abstract
The focus of this paper is the random sequences in the form \X0,X1, Xn=Xn-2+Xn-1,n=2,3,..\, referred to as Fibonacci Random Sequence (FRS). The initial random variables X0 and X1 are assumed to be absolutely continuous with joint probability density function (pdf) fX0,X1. The FRS is completely determined by X0 and X1 and the members of Fibonacci sequence \0,1,1,2,3,5,8,13,21,34,55,89,144,...\. We examine the distributional and limit properties of the random sequence Xn,n=0,1,2,... .
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