PreprintCC BY-NC-ND 4.0HAL
Global Central Limit Theorems for Markov chains with normal transition operator
Abstract
Let P be a Markov operator on a general state space (S,Σ) with invariant probability m, assumed ergodic. When P is normal in L2(m), we prove the necessity of uniform ergodicity, under some spectral conditions (satisfied when P is symmetric), for the annealed CLT to hold for {\it every} centered $ f \in L_2(m)$. We also obtain results without assuming normality under some Ritt-type conditions.
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BibTeX
@misc{cuny2026global,
title = {{Global Central Limit Theorems for Markov chains with normal transition operator}},
author = {Christophe Cuny and Michael Lin},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2610.02282},
eprint = {2610.02282},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05769894v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Global Central Limit Theorems for Markov chains with normal transition operator
AU - Christophe Cuny
AU - Michael Lin
PY - 2026
DA - 2026/09/30
PB - HAL
DO - 10.48550/arxiv.2610.02282
UR - https://hal.science/hal-05769894v1
AB - Let P be a Markov operator on a general state space (S,Σ) with invariant probability m, assumed ergodic. When P is normal in L_2(m), we prove the necessity of uniform ergodicity, under some spectral conditions (satisfied when P is symmetric), for the annealed CLT to hold for {\it every} centered $ f \in L_2(m)$. We also obtain results without assuming normality under some Ritt-type conditions.
ER -