Singles in a Markov chain. (English) Zbl 1199.60265

Let \(\{X_i\mid i\geq1\}\) be a sequence of random variables (taking values in the set \(\{0,1\})\) that forms a Markov chain with transition matrix \(P\) and with the initial distribution \((q,p)=(P(X_1=0),P(X_1=1))\). The authors study the number of singles in the vector \((X_1,X_2,\dots,X_n)\) (where a single in a sequence is an isolated value of \(0\) or \(1\)). Several asymptotic results, in particular a central limit theorem for the number of singles, are proved.


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