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Some New Results for the Tree Indexed Markov Chains

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

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.

Keywords

Tree-indexed markov chains Strong limit theorem Martingale difference sequence 

References

  1. 1.
    Benjiamini I, Peres Y (1994) Markov Chains indexed by trees. Ann Probab 22:219–243CrossRefMathSciNetGoogle Scholar
  2. 2.
    Zach D, Sunder S (2005) Large deviations for a class of nonhomogneous Markov chains. Ann Probab 15:421–486CrossRefMATHGoogle Scholar
  3. 3.
    Yang WG, Ye Z, Liu W (2006) A local convergence theorem for partial sums of stochastic adapted sequence. Czechoslovak Math J 56:525–532CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Yang W (2003) Some limit properties for Markov chains indexed by a homogeneous tree. Stat Probab Lett 65:241–250CrossRefMATHGoogle Scholar
  5. 5.
    Fan Z, Jin S, Bian J (2009) The recurrence for the tree indexed Markov chains. Math Pract Theory 39:221–223Google Scholar
  6. 6.
    Shi J (1999) The discrete martingale and its application, vol 35. The Science Press, Beijing, pp 743–745Google Scholar
  7. 7.
    Yang WG (2009) Strong law of large numbers for countable nonhomogeneous Markov Chains. Linear Algebra Appl 430:3008–3018CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Fan ZY, Zhai QL, Jin S (2010) Some limit properties for nonhomogeneous tree indexed Markov Chains. Proc CDEE 2010 2010:91–94Google Scholar
  9. 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 121–125Google Scholar
  10. 10.
    Isaac k (1999) On equitable ratios of dubins-freedman type. Stat Probab Lett 42:1–6CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Zhenyao Fan
    • 1
  • Jian Zhang
    • 1
  • Jing Bian
    • 1
  • Yourong Wang
    • 1
  1. 1.TangShan CollegeTangshanChina

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