Search Results

Journal: Annales Mathematicae Silesianae

Central limit theorem for random "contractive" functions on interval

Maciej Block , Wiktoria Kacprzak , Dorian Falęcki

Language: EN | Published: 26-04-2025 | 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]).

2025-04-26



Journal: Annales Mathematicae Silesianae

Global central limit theorems for stationary Markov chains

Michael Lin

Language: EN | Published: 20-05-2025 | Abstract | pp. 177-189

Let P be a Markov operator on a general state space (S, Σ) with an invariant probability measure m, assumed to be ergodic. We study conditions which yield that for every centered non-zero f ∈ L²(m) a non-degenerate annealed CLT and an L²-normalized CLT hold.

2025-05-20