Relative growth of the partial sums of certain random Fibonacci-like sequences

Alexander Roitershtein, Zhirou Zhou

We consider certain Fibonacci-like sequences $(X_n{)}_{n\ge 0}$ perturbed with a random noise. Our main result is that $\frac{1}{X_n}{\sum }_{k=0}^{n-1}{X}_k$ converges in distribution,…