2009
DOI: 10.1051/ps:2008009
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On the number of word occurrences in a semi-Markov sequence of letters

Abstract: Abstract. Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process {Zγ ; γ ∈ 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. Mathematics Subject Classification. 60K10, 60K20, 60C05, 60E05.

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Cited by 4 publications
(1 citation statement)
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“…Semi-Markov processes are an important class of stochastic processes that have been widely studied and applied in several fields, see e.g. [1,16,19,21]. In this paper we introduce a class of stochastic processes, called step semi-Markov processes (SSMP) that generalizes ordinary semi-Markov processes.…”
Section: Introductionmentioning
confidence: 99%
“…Semi-Markov processes are an important class of stochastic processes that have been widely studied and applied in several fields, see e.g. [1,16,19,21]. In this paper we introduce a class of stochastic processes, called step semi-Markov processes (SSMP) that generalizes ordinary semi-Markov processes.…”
Section: Introductionmentioning
confidence: 99%