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Oscillation properties of expected stopping times and stopping probabilities for patterns consisting of consecutive states in Markov chains. (English) Zbl 1456.60179
Summary: We investigate a Markov chain with a state space $$1, 2, \ldots, r$$ stopping at appearance of patterns consisting of two consecutive states. It is observed that the expected stopping times of the chain have surprising oscillating dependencies on starting positions. Analogously, the stopping probabilities also have oscillating dependencies on terminal states. In a nonstopping Markov chain the frequencies of appearances of two consecutive states are found explicitly.
##### MSC:
 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 05C81 Random walks on graphs
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##### References:
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