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Physical Sciences and Engineering Mathematics Analysis

A convergence theorem for random continued fractions

Article ID Journal Published Year Pages File Type
4606957 Journal of Approximation Theory 2015 8 Pages PDF
Abstract

Let K(an/bn) be a continued fraction with elements (an,bn)(an,bn) picked randomly and independently from (C∖{0})×C(C∖{0})×C according to some probability distribution μμ. We show that K(an/bn) converges generally with probability 1 under very mild conditions on the measure μμ.

Keywords
General convergenceLinear fractional transformations
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Preview
A convergence theorem for random continued fractions
Authors
Lisa Lorentzen,
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Journal of Approximation Theory
Journal: Journal of Approximation Theory
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