On the Lebesgue structure of the distribution of a random variable defined by continued $A_2$-fractions
Probability
2024-12-24 v1
Abstract
In this paper, we study the Lebesgue structure of the distribution of a random variable given in terms of a continued fraction with a two-symbol alphabet , also known as -fractions. We establish necessary and sufficient conditions for the distribution to be discrete and provide some sufficient conditions for its singularity. We also explore non-trivial metric properties of the -representation with the specified alphabet.
Keywords
Cite
@article{arxiv.2412.17430,
title = {On the Lebesgue structure of the distribution of a random variable defined by continued $A_2$-fractions},
author = {Pratsiovytyi Mykola and Makarchuk Oleg and Karvatskyi Dmytro},
journal= {arXiv preprint arXiv:2412.17430},
year = {2024}
}