Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Uniform limit theorems for Harris recurrent Markov chains
Download PDF
Download PDF
  • Published: December 1988

Uniform limit theorems for Harris recurrent Markov chains

  • Shlomo Levental1 

Probability Theory and Related Fields volume 80, pages 101–118 (1988)Cite this article

  • 198 Accesses

  • 15 Citations

  • Metrics details

Summary

We study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type. Then we apply those results to Harris recurrent Markov chains based on some ideas of K. Athreya, P. Ney and E. Nummelin.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Athreya, K., Ney, P.: A new approach to the limit theory of recurrent Markov chains. Trans. Am. Math. Soc. 245, 493–501 (1978)

    Google Scholar 

  2. Chung, K.L., Markov Chains with stationary transition probabilities. Berlin Heidelberg: Springer 1960

    Google Scholar 

  3. Dudley, R.M.: Universal Donsker classes and metric entropy. Ann. Probab. 15, 1306–1326 (1987)

    Google Scholar 

  4. Dudley, R.M.: A course on empirical processes. Lect. Notes Math. vol. 1097, pp. 1–142. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  5. Gine, E., Zinn, J.: Some limit theorems for empirical processes. Ann. Probab. 12, 929–989 (1984)

    Google Scholar 

  6. Glynn, P.W.: Some new results in regenerative process theory. Technical report 60. Dept. of Operation Research, Stanford CA, Stanford University 1982

    Google Scholar 

  7. Levental, S.: Uniform limit theorems. Ph.D. thesis. Madison, WI: University of Wisconsin 1986

  8. Nummelin, E.: General irreducible Markov chains and non-negative operators. Cambridge: Cambridge University Press 1984

    Google Scholar 

  9. Orey, S.: Lecture notes on limit theorems for Markov chain transition probabilities. London: Van Nostrand Reinhold 1971

    Google Scholar 

  10. Pollard, D.: A central limit theorem for empirical processes. J. Austral. Math. Soc., Ser A 33, 235–248 (1982)

    Google Scholar 

  11. Pollard, D.: Convergence of stochastic processes. Springer series in statistics. New York Berlin Heidelberg: Springer 1984

    Google Scholar 

  12. Ross, S.M.: Stochastic processes. New York: Wiley 1983

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, 48824-1027, East Lansing, MI, USA

    Shlomo Levental

Authors
  1. Shlomo Levental
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Levental, S. Uniform limit theorems for Harris recurrent Markov chains. Probab. Th. Rel. Fields 80, 101–118 (1988). https://doi.org/10.1007/BF00348754

Download citation

  • Received: 09 September 1986

  • Revised: 12 February 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00348754

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Markov Chain
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature