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A martingale proof of Dobrushin’s theorem for non-homogeneous Markov chains. (English) Zbl 1111.60057

Summary: R. L. Dobrushin [Teor. Veroyatn. Primen. 1, 72–89 and 365–425 (1956; Zbl 0093.15001)] proved an important central limit theorem for non-homogeneous Markov chains. In this note, a shorter and different proof elucidating more the assumptions is given through martingale approximation.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F05 Central limit and other weak theorems

Citations:

Zbl 0093.15001
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