Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-30T23:48:02.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Poisson limit law for Markov chains

Published online by Cambridge University Press:  19 September 2008

B. Pitskel
Get access Rights & Permissions [Opens in a new window]

Abstract

For a mixing stationary Markov chain we prove a Poisson limit law for the recurrence to small cylindrical sets. Since hyperbolic torus automorphisms are Markov chains, the result carries over to these transformations.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 501 - 513
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Sevast'yanov, B. A.. Poisson limit law for a scheme of sums of independent random variables. (Russian) Theory of Probability and its Applications. XVII (4) (1972), 695–699.Google Scholar
[2]Blum, J. R., Hanson, D. L. & Koopmans, L. H.. On the strong law of large numbers for a class of stochastic processes. Z. Wahrsch. verw. Gebrete. 2 (1963), 1–11.CrossRefGoogle Scholar
[3]Cornfeld, I. P., Fomin, S. V. & Sinai, Ya. G.. Ergodic Theory. Springer-Verlag, New York (1982).CrossRefGoogle Scholar
[4]Feller, W.. An Introduction to Probability Theory and Its Applications Vol. 1, 3rd ed., J. Wiley & Sons, New York (1968).Google Scholar
[5]Adler, R. & Weiss, B.. Entropy a complete metric invariant for automorphisms of the torus. Proc. Nat. Acad. Sci. USA 57 (6) (1967), 1573–1576.CrossRefGoogle ScholarPubMed