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The invariance principle for some class of Markov chains. (English. Russian original) Zbl 0966.60065

Theory Probab. Appl. 44, No. 1, 136-139 (1999); translation from Teor. Veroyatn. Primen. 44, No. 1, 151-154 (1999).
A Markov chain with state space \(\{-m,\dots, -1,0,1,\dots, m\}\) is considered. A number \(n\geq 1\) is assumed to exist such that all elements of the \(n\)-step transition matrix are positive. The invariance principle for this chain is proved, namely, the sequence of centered and normalized partial sums of members of this chain (considered as stepped processes on the interval \([0,1]\)) converges weakly to the Wiener process.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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