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Ruelle’s Perron-Frobenius theorem and the central limit theorem for additive functionals of one-dimensional Gibbs states. (English) Zbl 0679.60034
Adaptive statistical procedures and related topics, Proc. Symp., Upton/NY 1985, IMS Lect. Notes Monogr. Ser. 8, 428-446 (1986).
Summary: [For the entire collection see Zbl 0677.00025.]
A central limit theorem for a class of stationary sequences is given. The proof is based on the spectral analysis of an associated Perron-Frobenius type operator.

60F05 Central limit and other weak theorems
60F10 Large deviations
60G10 Stationary stochastic processes