On the convergence of stochastic Fibonacci series

Abstract

One very spesific case of linear second-order autoregressive sequence of random variables, the so-called stochastic Fibonacci sequence, is considered. For a random series, whose terms are properly normed partial sums of elements of the Fibonacci sequence, we study assumptions which garantee almost sure convergence of the introduced series. Obtained result is quite simple and understandable. In partcular, it implies that the Strong Law of Large Numbers for the Fibonacci sequence holds true.