Limit theorems for sums of partial quotients of continued fractions (Q1099487)

We prove that the partial quotients \(a_ j\) of the regular continued fraction expansion cannot satisfy a strong law of large numbers of any reasonably growing norming sequence, and that the \(a_ j\) belong to the domain of normal attraction to a stable law with characteristic exponent 1. We also show that the \(a_ j\) satisfy a central limit theorem if a few of the largest ones are trimmed.