Abstract
We consider certain Fibonacci-like sequences perturbed with a random noise. Our main result is that converges in distribution, as n goes to infinity, to a random variable W with Pareto-like distribution tails. We show that is a monotonically decreasing characteristic of the input noise, and hence can serve as a measure of its strength in the model. Heuristically, the heavy-tailed limiting distribution, versus a light-tailed one with can be interpreted as an evidence supporting the idea that the noise is ‘singular’ in the sense that it is ‘big’ even in a ‘slightly’ perturbed sequence.
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