The Annals of Probability

Random $f$-Expansions

Jon Aaronson

Full-text: Open access

Abstract

We consider the asymptotic distribution properties of $f$-expansion digits. In particular, if $x = 1/\varphi_0(x) - 1/\varphi_1(x) - \cdots$ etc., then $\frac{1}{n} \sum^{n-1}_{k=0} \varphi_k \rightarrow 3 \text{in measure}.$

Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 1037-1057.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992457

Digital Object Identifier
doi:10.1214/aop/1176992457

Mathematical Reviews number (MathSciNet)
MR841603

Zentralblatt MATH identifier
0658.60050

JSTOR
links.jstor.org

Subjects
Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx]

Keywords
28D 60F 60G $f$-expansions conservative ergodic measure preserving transformation stable laws Darling-Kac distributional limit theorem

Citation

Aaronson, Jon. Random $f$-Expansions. Ann. Probab. 14 (1986), no. 3, 1037--1057. doi:10.1214/aop/1176992457. https://projecteuclid.org/euclid.aop/1176992457


Export citation