Skip to main content

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 219))

  • 886 Accesses

Abstract

The strong limit theorem is one of the central questions for studying in the international Probability theory. The purpose of this paper is to give a strong limit theorem for functions of two-ordered Markov chains indexed by a kind of nonhomogeneous tree.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Benjiamini I, Peres Y (1994) Markov Chains indexed by trees. Ann Probab 22:219–243

    Article  MathSciNet  Google Scholar 

  2. Zach D, Sunder S (2005) Large deviations for a class of nonhomogneous Markov chains. Ann Probab 15:421–486

    Article  MATH  Google Scholar 

  3. Yang WG, Ye Z, Liu W (2006) A local convergence theorem for partial sums of stochastic adapted sequence. Czechoslovak Math J 56:525–532

    Article  MATH  MathSciNet  Google Scholar 

  4. Yang W (2003) Some limit properties for Markov chains indexed by a homogeneous tree. Stat Probab Lett 65:241–250

    Article  MATH  Google Scholar 

  5. Fan Z, Jin S, Bian J (2009) The recurrence for the tree indexed Markov chains. Math Pract Theory 39:221–223

    Google Scholar 

  6. Shi J (1999) The discrete martingale and its application, vol 35. The Science Press, Beijing, pp 743–745

    Google Scholar 

  7. Yang WG (2009) Strong law of large numbers for countable nonhomogeneous Markov Chains. Linear Algebra Appl 430:3008–3018

    Article  MATH  MathSciNet  Google Scholar 

  8. Fan ZY, Zhai QL, Jin S (2010) Some limit properties for nonhomogeneous tree indexed Markov Chains. Proc CDEE 2010 2010:91–94

    Google Scholar 

  9. Fan ZY, Jin S, Bian J (2009) A new application of stochastic matrices. The proceeding of 3th international workshop on matrix analysis, vol 1. World Academic Press, New York, pp 121–125

    Google Scholar 

  10. Isaac k (1999) On equitable ratios of dubins-freedman type. Stat Probab Lett 42:1–6

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhenyao Fan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag London

About this paper

Cite this paper

Fan, Z., Zhang, J., Bian, J., Wang, Y. (2013). Some New Results for the Tree Indexed Markov Chains. In: Zhong, Z. (eds) Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012. Lecture Notes in Electrical Engineering, vol 219. Springer, London. https://doi.org/10.1007/978-1-4471-4853-1_72

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-4853-1_72

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4852-4

  • Online ISBN: 978-1-4471-4853-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics