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A generalized notion of variation applied to Markov chains and Anosov maps
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  • Published: December 1995

A generalized notion of variation applied to Markov chains and Anosov maps

  • J. Loviscach1 

Probability Theory and Related Fields volume 103, pages 553–570 (1995)Cite this article

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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.

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References

  1. Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Berlin: Springer 1975

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  2. 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.

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  3. 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)

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  4. Kato, T.: Perturbation theory for linear operators. New York: Springer 1966

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  5. Loviscach, Jörn: Probabilistic models of multidimensional piecewise expanding mappings. J. Stat. Phys.75 189–213 (1994)

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Authors and Affiliations

  1. BiBoS, Fakultät für Physik, Universität Bielefeld, D-33615, Bielefeld, Germany

    J. Loviscach

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  1. J. Loviscach
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work supported by Studienstiftung des deutschen Volkes

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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

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  • Received: 26 April 1994

  • Revised: 01 November 1994

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01246339

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Mathematics Subject Classifications

  • 60F05
  • 58F15
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