On beta distributed limits of iterated linear random functions

Shaun McKinlay

Statistics & Probability Letters, 2017, vol. 127, issue C, 33-41

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.

Keywords: Iterated random functions; Nested interval schemes; Markov chains; Interval splitting; Random equations; Beta distribution (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.03.021

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