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A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments. (English) Zbl 1316.60039
Summary: We consider strong limit theorems for Markov chains in bi-infinite random environments. We first give a new proof of a strong limit theorem of W. Liu and W. Yang [Stat. Probab. Lett. 22, No. 4, 295–301 (1995; Zbl 0833.60034)] on the average of functions of non-homogeneous Markov chains by constructing a nonnegative martingale. As corollaries, for a Markov chain in a bi-infinite random environment, we obtain strong limit theorems for the conditional relative entropy and for the number of times that the Markov chain and related processes reach a given point.
MSC:
60F15 Strong limit theorems
60K37 Processes in random environments
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F05 Central limit and other weak theorems
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