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- Title
Waiting Time Problems for Patterns in a Sequence of Multi-State Trials.
- Authors
Kim, Bara; Kim, Jeongsim; Kim, Jerim
- 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.
- Subjects
MATRIX analytic methods; GENERATING functions; MARKOV processes; MARTINGALES (Mathematics)
- Publication
Mathematics (2227-7390), 2020, Vol 8, Issue 11, p1893
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math8111893