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A strong limit theorem for the harmonic mean of the random transition probabilities of finite nonhomogeneous Markov chains. (Chinese. English summary) Zbl 0964.60024

Summary: Let \(\{X_n, n\geq 0\}\) be a nonhomogeneous Markov chain with state space \(I= \{1,\dots, N\}\) and transition probabilities \(p_n(i,j)= P(X_n= j\mid X_{n-1}= i)\). Conditions that the harmonic mean of random transition probabilities \(p_1(X_0, X_1),\dots, p_n(X_{n-1}, X_n)\) 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.

MSC:

60F15 Strong limit theorems
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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