• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.541-553
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• 2012

In this paper, we study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain on the generalized gambling system indexed by a tree by constructing a nonnegative martingale. As corollary, we obtain the property of the harmonic mean and the arithmetic mean of random transition probability for a second-order nonhomogeneous Markov chain indexed by a double root tree.