Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SOME GENERALIZED SHANNON-MCMILLAN THEOREMS FOR NONHOMOGENEOUS MARKOV CHAINS ON SECOND-ORDER GAMBLING SYSTEMS INDEXED BY AN INFINITE TREE WITH UNIFORMLY BOUNDED DEGREE

  • Wang, Kangkang (School of Mathematics and Physics, Jiangsu University of Science and Technology) ;
  • Xu, Zurun (School of Mathematics and Physics, Jiangsu University of Science and Technology)
  • Received : 2010.12.09
  • Accepted : 2011.08.12
  • Published : 2012.01.30
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Abstract

In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.

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References

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