On limit theorems for continued fractions
Zbigniew S. Szewczak
TL;DR
This paper establishes that classical limit theorems like the weak law of large numbers and the domain of attraction of the normal law apply to sums of functionals of digits in continued fraction expansions.
Contribution
It extends fundamental probabilistic limit theorems to the setting of continued fraction digit functionals, providing new theoretical insights.
Findings
Weak laws of large numbers hold for sums of continued fraction digit functionals.
The domain of attraction of the normal law is characterized for these sums.
Classical limit theorems are applicable in this context.
Abstract
It is shown that for sums of functionals of digits in continued fraction expansion the Kolmogorov-Feller weak laws of large numbers and the Khinchine-L\'evy-Feller-Raikov characterization of the domain of attraction of the normal law hold.
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