Central limit asymptotics for shifts of finite type
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. \textit{Y. Guivarc'h} and \textit{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. \textit{J. Rousseau-Egele}, Ann. Probab. 11, 772-788 (1983; Zbl 0518.60033)].
scientific article; zbMATH DE number 4149258