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MR2828040 60F15 (60J10 60K37)
Li, Ying Qiu; Wang, He Song; Wang, Zhong Some strong limit theorems of geometric average of transition probabilities and their function for Markov chains in Markovian environments. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 31 (2011), no. 2, 508–517.
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