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Central limit asymptotics for shifts of finite type. (English) Zbl 0701.60026
The authors prove the Berry-Esséen bound in the central limit theorem for Hölder-continuous functions on a shift of finite type endowed with a Gibbs measure [cf. Y. Guivarc’h and J. Hardy, Ann. Inst. Henri Poincaré, Probab. Stat. 24, 73-98 (1988; Zbl 0649.60041)]. Moreover, if f has a non lattice distribution the asymptotic expansion up to order o(1/\(\sqrt{n})\) is determined, and under certain moment conditions higher order approximations are derived.
The method of proof is based on the theory of Perron-Frobenius operators [cf. J. Rousseau-Egele, Ann. Probab. 11, 772-788 (1983; Zbl 0518.60033)].
Reviewer: M.Denker

MSC:
60F99 Limit theorems in probability theory
28D20 Entropy and other invariants
60K35 Interacting random processes; statistical mechanics type models; percolation theory
54H20 Topological dynamics (MSC2010)
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