On a Gauss-Kuzmin Type Problem for a Family of Continued Fractions
Number Theory
2013-09-19 v2 Probability
Abstract
We study a family of continued fraction expansion of reals from the unit interval. The Perron-Frobenius operator of the transformation which generates this expansion under the invariant measure of this transformation is given. Using the ergodic behavior of homogeneous random system with complete connections associated with this expansion we solve a variant of Gauss-Kuzmin problem for this continued fraction expansion.
Keywords
Cite
@article{arxiv.1010.4864,
title = {On a Gauss-Kuzmin Type Problem for a Family of Continued Fractions},
author = {Dan Lascu},
journal= {arXiv preprint arXiv:1010.4864},
year = {2013}
}
Comments
15 pages, Chapter 4 of my PhD thesis