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On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes (2505.01045v1)
Published 2 May 2025 in math.PR
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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