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On beta distributed limits of iterated linear random functions

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  • McKinlay, Shaun

Abstract

We consider several special cases of iterations of random i.i.d. linear functions with beta distributed fixed points. When iterated in a backward direction we obtain a nested interval scheme, whilst the forward direction generates an ergodic Markov chain. Our approach involves relating the random equation satisfied by the beta distributed fixed point to a random equation with a gamma distributed fixed point. The paper extends many results available in the existing literature.

Suggested Citation

  • McKinlay, Shaun, 2017. "On beta distributed limits of iterated linear random functions," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 33-41.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:33-41
    DOI: 10.1016/j.spl.2017.03.021
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    References listed on IDEAS

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    1. Stoyanov, Jordan & Pirinsky, Christo, 2000. "Random motions, classes of ergodic Markov chains and beta distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 293-304, November.
    2. Pacheco-González, Carlos G., 2009. "Ergodicity of a bounded Markov chain with attractiveness towards the centre," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2177-2181, October.
    3. Dyszewski, Piotr, 2016. "Iterated random functions and slowly varying tails," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 392-413.
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    5. Stefano M. Iacus & Ilia Negri, 2003. "Estimating unobservable signal by Markovian noise induction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(2), pages 153-167, December.
    6. Devroye, Luc & Letac, Gerard & Seshadri, Vanamamalai, 1986. "The limit behavior of an interval splitting scheme," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 183-186, June.
    7. McVinish, R. & Pollett, P.K. & Chan, Y.S., 2016. "A metapopulation model with Markovian landscape dynamics," Theoretical Population Biology, Elsevier, vol. 112(C), pages 80-96.
    8. Johnson, Norman L. & Kotz, Samuel, 1995. "Use of moments in studies of limit distributions arising from iterated random subdivisions of an interval," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 111-119, August.
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