Nonhomogeneous Markov chain,Random transition probability, Harmonic mean, Differentiation on a net,Strong limit theorem.
,"/> A Strong Limit Theorem for the Harmonic Mean of the Random Transition Probabilities of Finite Nonhomogeneous Markov Chains  

Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (1): 81-84.

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A Strong Limit Theorem for the Harmonic Mean of the Random Transition Probabilities of Finite Nonhomogeneous Markov Chains  

  

  1. Department of Mathematics, Hebei University of Technology,Tianjin 300130
  • Online:2000-01-07 Published:2000-01-07

Abstract:

 Let {Xn, n≥0} be a nonhomogeneous Markov chain with state space I = {1, 2, …, N} and transition probabilities pn(i, j) = P(X n =j|Xn-1 = i). In this paper the conditions that the harmonic mean of random transition probabilities p1(X0,X1),…, pn (Xn-1,Xn) converges to 1/N a.s. are investigated, and the differentiation technique on a net together with the tool of generating function for the study of strong limit theorems of Markov chains is presented.

Key words:  Nonhomogeneous Markov chain')"> Nonhomogeneous Markov chain, Random transition probability, Harmonic mean, Differentiation on a net, Strong limit theorem.

CLC Number: 

  • 60F
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