This note demonstrates how the central limit theorem applies to ergodic Markov processes, indicating new implications for semigroup theory.
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) studied this question.
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