Skip to main content

Recent results on mixing in topological measure spaces

  • 740 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 89)

Keywords

  • Markov Chain
  • Discrete Time Markov Chain
  • Symmetrical Random Walk
  • Markovian Transition Matrix
  • Discrete Random Walk

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Böge, W., Krickeberg, K., and F. Papangelou: Über die dem Lebesgueschen Maß isomorphen topologischen Maße. To appear.

    Google Scholar 

  2. Kai Lai Chung and P. Erdös: Probability limit theorems assuming only the first moment. Mem. Amer. Math. Soc. 6, 1–19 (1951).

    MathSciNet  MATH  Google Scholar 

  3. Gillis, J.: Centrally biased discrete random walk. Quart. J. Math. Oxford Ser. (2) 7, 144–152 (1956).

    MathSciNet  MATH  Google Scholar 

  4. Hajian, A. B. and S. Kakutani: Weakly wandering sets and invariant measures. Trans. Amer. Math. Soc. 110, 136–151 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Hopf, E.: Ergodentheorie. Berlin 1937.

    Google Scholar 

  6. Kakutani, S. and W. Parry: Infinite measure preserving transformations with “mixing”. Bull. Amer. Math. Soc. 69, 752–756 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Kemeny, J. G.: A probability limit theorem requiring no moments. Proc. Amer. Math. Soc. 10, 607–612 (1959).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kingman, J. F. C. and S. Orey: Ratio limit theorems for Markov chains. Proc. Amer. Math. Soc. 15, 907–910 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Krickeberg, K.: Strong mixing properties of Markov chains with infinite invariant measure. Proc. Fifth Berkeley Symp. Math. Statist. Probability, Berkeley and Los Angeles 1966, Vol. I, Part II, 431–446.

    Google Scholar 

  10. Krickeberg, K.: Mischende Transformationen auf Mannigfaltigkeiten unendlichen Maßes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 7, 235–247 (1967).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Papangelou, F.: Strong ratio limits, R-recurrence and mixing properties of discrete parameter Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 8, 259–297 (1967).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Pruitt, W. E.: Strong ratio limit property for R-recurrent Markov chains. Proc. Amer. Math. Soc. 16, 196–200 (1965).

    MathSciNet  MATH  Google Scholar 

  13. Vere-Jones, D.: Geometric ergodicity in denumerable Markov chains. Quart. J. Math. Oxford Ser. 2, 13, 7–28 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1969 Springer-Verlag

About this paper

Cite this paper

Krickeberg, K. (1969). Recent results on mixing in topological measure spaces. In: Behara, M., Krickeberg, K., Wolfowitz, J. (eds) Probability and Information Theory. Lecture Notes in Mathematics, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079125

Download citation

  • DOI: https://doi.org/10.1007/BFb0079125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04608-0

  • Online ISBN: 978-3-540-36098-8

  • eBook Packages: Springer Book Archive