Random $f$-Expansions

Jon Aaronson

doi:10.1214/aop/1176992457

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Home > Journals > Ann. Probab. > Volume 14 > Issue 3 > Article

July, 1986 Random $f$-Expansions

Jon Aaronson

Ann. Probab. 14(3): 1037-1057 (July, 1986). DOI: 10.1214/aop/1176992457

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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 $\frac{1}{n} \sum^{n-1}_{k=0} \varphi_k \rightarrow 3 \text{in measure}.$

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Jon Aaronson. "Random $f$-Expansions." Ann. Probab. 14 (3) 1037 - 1057, July, 1986. https://doi.org/10.1214/aop/1176992457

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Published: July, 1986

First available in Project Euclid: 19 April 2007

zbMATH: 0658.60050

MathSciNet: MR841603

Digital Object Identifier: 10.1214/aop/1176992457

Subjects:

Primary: 47A35

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

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