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On the number of word occurrences in a semi-Markov sequence of letters. (English) Zbl 1181.60130

Summary: Let a finite alphabet \(\Omega\). We consider a sequence of letters from \(\Omega\) generated by a discrete time semi-Markov process \(\{Z_{\gamma};\gamma\in \mathbb N\}\). We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
60C05 Combinatorial probability
60E05 Probability distributions: general theory
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References:

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