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Waiting Time Problems for Patterns in a Sequence of Multi-State Trials

Authors
Kim, BaraKim, JeongsimKim, Jerim
Issue Date
11월-2020
Publisher
MDPI
Keywords
pattern; sooner waiting time; stopping probability; matrix analytic method
Citation
MATHEMATICS, v.8, no.11
Indexed
SCIE
SCOPUS
Journal Title
MATHEMATICS
Volume
8
Number
11
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/52056
DOI
10.3390/math8111893
ISSN
2227-7390
Abstract
In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.
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