GLOBAL CENTRAL LIMIT THEOREMS FOR STATIONARY MARKOV CHAINS

Michael Lin

doi:10.2478/amsil-2025-0011

GLOBAL CENTRAL LIMIT THEOREMS FOR STATIONARY MARKOV CHAINS

Michael Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 a L²(m) a non-degenerate annealed CLT and an L²-normalized CLT hold.

Original language	English
Journal	Annales Mathematicae Silesianae
DOIs	https://doi.org/10.2478/amsil-2025-0011
State	Accepted/In press - 1 Jan 2025

Keywords

Annealed clt
Central limit theorems
Stationary markov chains
Uniform ergodicity
Ρ-mixing

ASJC Scopus subject areas

General Mathematics

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10.2478/amsil-2025-0011

Cite this

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title = "GLOBAL CENTRAL LIMIT THEOREMS FOR STATIONARY MARKOV CHAINS",

abstract = "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 a L2(m) a non-degenerate annealed CLT and an L2-normalized CLT hold.",

keywords = "Annealed clt, Central limit theorems, Stationary markov chains, Uniform ergodicity, Ρ-mixing",

author = "Michael Lin",

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AB - 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 a L2(m) a non-degenerate annealed CLT and an L2-normalized CLT hold.

KW - Annealed clt

KW - Central limit theorems

KW - Stationary markov chains

KW - Uniform ergodicity

KW - Ρ-mixing

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GLOBAL CENTRAL LIMIT THEOREMS FOR STATIONARY MARKOV CHAINS

Abstract

Keywords

ASJC Scopus subject areas

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