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**Semi-Markov chains and hidden semi-Markov models toward applications. Their use in reliability and DNA analysis.**
*(English)*
Zbl 1208.60001

Lecture Notes in Statistics 191. New York, NY: Springer (ISBN 978-0-387-73171-1/pbk; 978-0-387-73173-5/ebook). xiii, 224 p. (2008).

Publisher’s description: This book is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. Another unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis.

The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers. It can also serve as a text for a six month research-oriented course at a Master or PhD level. The prerequisites are a background in probability theory and finite state space Markov chains.

The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers. It can also serve as a text for a six month research-oriented course at a Master or PhD level. The prerequisites are a background in probability theory and finite state space Markov chains.

### MSC:

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60K15 | Markov renewal processes, semi-Markov processes |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |

92D20 | Protein sequences, DNA sequences |

91B25 | Asset pricing models (MSC2010) |