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February 2021 Sieving random iterative function systems
Alexander Marynych, Ilya Molchanov
Bernoulli 27(1): 34-65 (February 2021). DOI: 10.3150/20-BEJ1221

Abstract

It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space components, it is possible to construct a scale invariant stochastic process. We study its distribution and paths properties. In particular, we show that it is càdlàg and has finite total variation. We also provide examples and analyse various properties of particular sieved iterative function systems including perpetuities and infinite Bernoulli convolutions, iterations of maximum, and random continued fractions.

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Alexander Marynych. Ilya Molchanov. "Sieving random iterative function systems." Bernoulli 27 (1) 34 - 65, February 2021. https://doi.org/10.3150/20-BEJ1221

Information

Received: 1 August 2019; Revised: 1 February 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282841
MathSciNet: MR4177360
Digital Object Identifier: 10.3150/20-BEJ1221

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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