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Antisymmetric functionals of reversible Markov processes. (English) Zbl 0813.60023
Summary: We prove the central limit theorem and invariance principle for antisymmetric functionals of ergodic reversible Markov processes under extremely mild conditions. Moreover, the proof is based upon an elementary, direct decomposition of the functional, into the sum of a martingale term and an asymptotically negligible term, by an analysis relying almost solely on symmetry considerations.

MSC:
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
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