## Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA AnalysisHere is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A 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. |

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### Contents

1 | |

DiscreteTime Renewal Processes | 17 |

SemiMarkov Chains | 42 |

Nonparametric Estimation for SemiMarkov Chains | 75 |

Reliability Theory for DiscreteTime SemiMarkov Systems | 101 |

Hidden SemiMarkov Model and Estimation | 131 |

Lemmas for SemiMarkov Chains | 179 |

Lemmas for Hidden SemiMarkov Chains | 183 |

### Other editions - View all

Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their ... Vlad Stefan Barbu,Nikolaos Limnios No preview available - 2008 |

### Common terms and phrases

algorithm aperiodic applications Assumptions A1 asymptotic normality asymptotic properties asymptotic variance Barbu chapter compute conditional distribution consider continuous-time convergence convolution CpG islands defined Definition delayed renewal chain denote diag(Q discrete discrete-time semi-Markov system EM algorithm embedded Markov chain expression failure rate given hidden Markov models hidden semi-Markov chain hidden semi-Markov models i,je initial distribution kernel q Lemma likelihood function Limnios Markov chain Markov processes Markov renewal chain Markov renewal equation martingales matrix-valued function ME(N mean sojourn MTTF obtain parameter positive integer probability Proof Proposition qij(k qu(k random variables recurrent renewal chain reliability renewal process renewal theorem sample path semi-Markov kernel semi-Markov processes semi-Markov transition sequence sojourn time distributions Springer Science+Business Media stationary distribution strongly consistent tends to infinity transition function transition matrix true value vector XL XL Yn)neN