Central Limit Theorem for Random “Contractive” Functions on Interval

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]).

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Publication Details

Journal
Annales Mathematicae Silesianae
Published
2025-04-26
DOI
https://doi.org/10.2478/amsil-2025-0005
Primary Topic
Stochastic processes and financial applications
Type
article
Field-Weighted Citation Impact
0.00
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article

Central Limit Theorem for Random “Contractive” Functions on Interval

M. Block, Wiktoria Kacprzak, Dorian Falęcki
Annales Mathematicae Silesianae
Stochastic processes and financial applications
article

Central Limit Theorem for Random “Contractive” Functions on Interval

M. Block, Wiktoria Kacprzak, Dorian Falęcki
article en

Abstract

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]).

Annales Mathematicae SilesianaeVol. 40(1)
Gdańsk University of Technology (PL)
Openalex Percentile: Top 89%
Stochastic processes and financial applications
DOIOpen Access PDFOpenAlex
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Central Limit Theorem for Random “Contractive” Functions on Interval — M. Block, Wiktoria Kacprzak, et al. · Annales Mathematicae Silesianae (2025) | TGRS Research Map | TGRS