Summary
Extending the operator formalism of [3] we show that there exists a large class of functions which possess an exponential decay of correlations and fulfill a central limit theorem under a certain type of Markov chains. This result can be applied to the symbolic dynamics of Anosov maps, showing that in the case of a absolutely continuous invariant measure there is a large class of functions with good ergodic properties-larger than the usual class of Hölder continuous functions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Berlin: Springer 1975
Blank, M.L.: Chaotic mappings and stochastic Markov chains. In: Mathematical Physics X. Proceedings, Leipzig 1991, pp. 341–345. Berlin: Springer 1992, ed. Schmüdgen, K.
Guivarc'h, Y., Hardy, J.: Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov. Ann. Inst. H. Poincaré24, 73–98 (1988)
Kato, T.: Perturbation theory for linear operators. New York: Springer 1966
Loviscach, Jörn: Probabilistic models of multidimensional piecewise expanding mappings. J. Stat. Phys.75 189–213 (1994)
Norman, F.: Markov processes and learning models. New York: Academic Press 1972
Author information
Authors and Affiliations
Additional information
work supported by Studienstiftung des deutschen Volkes
Rights and permissions
About this article
Cite this article
Loviscach, J. A generalized notion of variation applied to Markov chains and Anosov maps. Probab. Th. Rel. Fields 103, 553–570 (1995). https://doi.org/10.1007/BF01246339
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01246339