English

A note on Fibonacci Sequences of Random Variables

Other Statistics 2019-02-27 v1

Abstract

The focus of this paper is the random sequences in the form {X0,X1,\{X_{0},X_{1}, Xn=Xn2+Xn1,n=2,3,..}˙,X_{n}=X_{n-2}+X_{n-1},n=2,3,..\dot{\}}, referred to as Fibonacci Random Sequence (FRS). The initial random variables X0X_{0} and X1X_{1} are assumed to be absolutely continuous with joint probability density function (pdf) fX0,X1.f_{X_{0},X_{1}}. The FRS is completely determined by X0X_{0} and X1X_{1} and the members of Fibonacci sequence ϝ{0,1,1,2,3,5,8,13,21,34,55,89,144,...}.\digamma \equiv\{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,...X_{n},n=0,1,2,... .

Cite

@article{arxiv.1902.09790,
  title  = {A note on Fibonacci Sequences of Random Variables},
  author = {Ismihan Bayramoglu},
  journal= {arXiv preprint arXiv:1902.09790},
  year   = {2019}
}
R2 v1 2026-06-23T07:51:22.693Z