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A limit property of random conditional probabilities

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  • Liu, Wen

Abstract

Let {Xn,n[greater-or-equal, slanted]0} be a sequence of random variables taking values in S={1,2,...,N}, and let pk(xk x0,...,xk-1)=P(Xk=xk X0=x0,...,Xk-1=xk-1). In this paper a theorem on a.e. convergence for the harmonic mean of the random conditional probabilities {pk(Xk X0,...,Xk-1), 1[less-than-or-equals, slant]k[less-than-or-equals, slant]n} is obtained by using the tool of the conditional moment generating function and the differentiation on a net.

Suggested Citation

  • Liu, Wen, 2000. "A limit property of random conditional probabilities," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 299-304, September.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:3:p:299-304
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    References listed on IDEAS

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    1. Wen, Liu, 1994. "Some strong limit theorems relative to the geometric average of random transition probabilities of arbitrary finite nonhomogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 21(1), pages 77-83, September.
    2. Wen, Liu & Weiguo, Yang, 1996. "An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 129-145, January.
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    Cited by:

    1. Liu, Wen, 2003. "Some limit properties of the multivariate function sequences of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 41-50, January.

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    1. Liu, Wen, 2003. "Some limit properties of the multivariate function sequences of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 41-50, January.

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