Bhattacharya's theorem implies the Kipnis-Varadhan functional CLT for reversible ergodic Markov processes via semigroup theory incorporated into the generator's range condition.
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On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes
Bhattacharya's theorem implies the Kipnis-Varadhan functional CLT for reversible ergodic Markov processes via semigroup theory incorporated into the generator's range condition.