On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes

Edward C Waymire

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arXiv · 2505.01045

On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes

Edward C Waymire

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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.

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Edward C Waymire. 2025-05-02. On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes. https://arxiv.org/abs/2505.01045

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