Abstract
Let T be a measure-preserving transformation of a probability space (X, F, μ) and let A be the generator of a μ-symmetric Markov process with state space X. Under the assumption that A is an “eigenvector” for T an extension of T is constructed in terms of A. By means of this extension a version of the central limit theorem is proved via approximation by martingales. Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. I. Gordin, “On the central limit theorem for stationary processes,”Dokl. Akad. Nauk SSSR,188, No. 1, 739–741 (1969).
M. Gordin, “Homoclinic approach to the central limit theorem for dynamical systems,”Contemp. Math.,149, 149–162 (1993).
Sh. Ito, “A construction of transversal flows for maximal Markov automorphisms,” in:Proceedings of the Second Japan-USSR Symposium on Probability Theory, Vol. 3 (1972).
V. P. Leonov,Some Applications of Higher Semi-Invariants to the Theory of Random Processes [in Russian], Nauka, Moscow (1964).
V. A. Rokhlin, “Lectures in the entropy theory of measure-preserving transformations,”Usp. Mat. Nauk,22, No. 5, 1–56 (1967).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 10–19.
Translated by V. Sudakov.
Rights and permissions
About this article
Cite this article
Gordin, M.I. Extensions of dynamical systems and the martingale approximation method. J Math Sci 88, 7–12 (1998). https://doi.org/10.1007/BF02363256
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02363256