On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes
Probability
2026-04-14 v2
Abstract
In this note, the time reversible case of a general theorem of Bhattacharya is shown to imply the Kipnis-Varadhan functional central limit theorem for ergodic Markov processes. To this end, a few results from semigroup theory, including the resolvent identity, are incoporated in Bhattacharya's range condition for the inifinitesimal generator.
Keywords
Cite
@article{arxiv.2505.01045,
title = {On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes},
author = {Edward C Waymire},
journal= {arXiv preprint arXiv:2505.01045},
year = {2026}
}
Comments
This is a replacement in which an application of the method has been added to obtain an extended law of the iterated logarithm