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A homoclinic version of the central limit theorem

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Abstract

The definitions of homoclinic partitions and transformations are given in situations that are standard for topological dynamics and ergodic theory. A variant of the central limit theorem is proved, the formulation of which makes use of homoclinic transformations.

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References

  1. R. Bouen (R. Bowen), Methods of Symbolic Dynamics, Moscow (1979).

  2. V. P. Leonov, Some Applications of the Higher Semiinvariants to the Theory of Stationary Random Processes [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  3. Z. Nitecki, Differential Dynamics. An Introduction to the Orbit Structure of Diffeomorphisms, The MIT Press, Cambridge, Mass. (1971).

    Google Scholar 

  4. J. Feldman and C. C. Moore, "Ergodic equivalence relations, cohomology, and von Neumann algebras. I," Trans. Amer. Math. Soc.,234, No. 2, 289–324 (1977).

    Google Scholar 

  5. C. Stein, "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables," in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II, Probability Theory, Univ. California Press, Berkeley, Calif. (1972), pp. 583–602

    Google Scholar 

  6. Sh. Ito, "A construction of transversal flows for maximal Markov automorphisms," in: Proc. Second Japan—USSR Symposium on Probability Theory (Kyoto, 1972), Part II, Probability Group, Kyoto (1972), pp. 12–17.

    Google Scholar 

  7. M. I. Gordin, "Homoclinic transformations and the central limit theorem," in: Abstracts of Reports at the Fifth Vilnius Conference on Probability Theory and Mathematical Statistics, Vol. 3, Vilnius (1989), pp. 156–157.

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Authors
  1. M. I. Gordin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 80–91, 1990.

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Gordin, M.I. A homoclinic version of the central limit theorem. J Math Sci 68, 451–458 (1994). https://doi.org/10.1007/BF01254269

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  • DOI: https://doi.org/10.1007/BF01254269

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