Central Limit Theorem for Random “Contractive” Functions on Interval

Maciej Block; Wiktoria Kacprzak; Dorian Falęcki

doi:10.2478/amsil-2025-0005

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Central Limit Theorem for Random “Contractive” Functions on Interval

Annales Mathematicae Silesianae

Volume 40 (2026): Issue 1 (March 2026)

By: Maciej Block, Wiktoria Kacprzak and Dorian Falęcki

Open Access

|Apr 2025

Abstract

We use the approach from Czudek and Szarek (see [1]) to prove the central limit theorem for a stationary Markov chain generated by an iterative function system for a family of increasing, injective functions on [0, 1] with “contractive” properties. We introduce a new approach to prove existence of an unique invariant measure using e-property (see [2]).

References

K. Czudek and T. Szarek, Ergodicity and central limit theorem for random interval homeomorphisms, Israel J. Math. 239 (2020), no. 1, 75–98. DOI: 10.1007/s11856-020-2046-4.
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T. Komorowski, Sz. Peszat, and T. Szarek, On ergodicity of some Markov processes, Ann. Probab. 38 (2010), no. 4, 1401–1443. DOI: 10.1214/09-AOP513.
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G. Łuczyńska, Ergodyczność oraz twierdzenia graniczne dla stochastycznych układów dynamicznych na okręgu, PhD thesis, Uniwersytet Gdański, Gdańsk, 2022.
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D. Malicet, Random walks on Homeo(S¹), Comm. Math. Phys. 356 (2017), no. 3, 1083–1116.
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M. Maxwell and M. Woodroofe, Central limit theorems for additive functionals of Markov chains, Ann. Probab. 28 (2000), no. 2, 713–724.
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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2025-0005 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 1 - 12

Submitted on: Dec 26, 2024

Accepted on: Mar 12, 2025

Published on: Apr 26, 2025

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

60F05,

60J25,

37A25

Related subjects:

Mathematics,

General mathematics

© 2025 Maciej Block, Wiktoria Kacprzak, Dorian Falęcki, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 40 (2026): Issue 1 (March 2026)