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Dynamics of Random Continued Fractions

Borwein, Jonathan M. and Luke, D. Russell (2005) Dynamics of Random Continued Fractions. Abstract and Applied Analysis, 5 . pp. 449-468.

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    Abstract

    We study a generalization of a continued fraction of Ramanujan with random coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so divergence of their corresponding continued fractions.

    Item Type: Article
    Additional Information: pubdom TRUE
    Uncontrolled Keywords: Continued fractions, Ramanujan AGM relation, stochastic difference equations
    Subjects: 11-xx Number theory > 11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms
    Faculty: UNSPECIFIED
    Depositing User: Russell Luke
    Date Deposited: 14 Mar 2005
    Last Modified: 12 Jan 2015 14:03
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/275

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