English

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

R2 v1 2026-06-28T23:18:52.977Z