Skip to main content
SpringerLink
Log in
Book cover

Contributions to Stochastics pp 184–186Cite as

A Short Proof for the Contraction-Property of Markov Chains with Attractive States

  • Chapter

  • 131 Accesses

Summary

A short proof for the contraction-property of the map TP = P.P for homogeneous Markov chains with attractive states is presented 1). It enables the application of Banach’s fixed point theorem to show the existence of the stable distribution. This approach may serve as an alternative for the classic approach (cf. [1], chapter v.2) presented in postcalculus texts on the basics of Markov chains.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • 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

References

  1. Doob, J.L.: Stochastic processes. John Wiley, New York 1953 (7th printing, 1967 ).

    Google Scholar 

  2. Jacobs, K.: Markov-Prozesse mit endlichvielen Zuständen. Entry from K. Jacobs (edt.): Selecta Mathematika IV. Springer, Berlin 1972.

    Google Scholar 

  3. Markov, A.A.: Investigations of a notable case of dependent trials (in Russian). Izvestia Akad. Nauk S.P.-B.(6), 1, 61–80 (1907).

    Google Scholar 

  4. Ssterreicher, F. and M. Thaler: Analysing Markov chains by risk sets. Studia Sci. Math. Hungar. 15, 411–419 (1980).

    Google Scholar 

  5. Seneta, E.: Non-negative matrices and Markov chains. Springer, New York 1981 (2nd edition).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Salzburg, A-5020, Salzburg, Austria

    Ferdinand Österreicher

Authors
  1. Ferdinand Österreicher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich IV/Mathematik, Universität Trier, Postfach 38 25, 5500, Trier, Germany

    Wolfgang Sendler

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Physica-Verlag Heidelberg

About this chapter

Cite this chapter

Österreicher, F. (1987). A Short Proof for the Contraction-Property of Markov Chains with Attractive States. In: Sendler, W. (eds) Contributions to Stochastics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46893-3_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46893-3_18

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-642-46895-7

  • Online ISBN: 978-3-642-46893-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation