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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. Vlad Stefan Barbu is associate professor in statistics at the University of Rouen, France, Laboratory of Mathematics ‘Raphaël Salem.’ His research focuses basically on stochastic processes and associated statistical problems, with a particular interest in reliability and DNA analysis. He has published several papers in the field. Nikolaos Limnios is a professor in Applied Mathematics at the University of Technology of Compiègne. His research interest concerns stochastic processes and statistics with application to reliability. He is the co-author of the books: Semi-Markov Processes and Reliability (Birkhäuser, 2001 with G. Oprisan) and Stochastic Systems in Merging Phase Space (World Scientific, 2005, with V.S. Koroliuk).

Markov processes --- Reliability (Engineering) --- DNA --- Markov, Processus de --- Fiabilité --- Mathematical models --- Analysis --- Modèles mathématiques --- DNA --Analysis --Mathematical models. --- Markov processes. --- Reliability (Engineering) --Mathematical models. --- Evaluation Studies as Topic --- Probability --- Stochastic Processes --- Epidemiologic Research Design --- Investigative Techniques --- Nucleic Acids --- Statistics as Topic --- Mathematical Concepts --- Nucleic Acids, Nucleotides, and Nucleosides --- Epidemiologic Methods --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Health Care Evaluation Mechanisms --- Quality of Health Care --- Public Health --- Phenomena and Processes --- Chemicals and Drugs --- Environment and Public Health --- Health Care Quality, Access, and Evaluation --- Health Care --- Markov Chains --- Models, Theoretical --- Reproducibility of Results --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models. --- Fiabilité --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Deoxyribonucleic acid --- Desoxyribonucleic acid --- Thymonucleic acid --- TNA (Nucleic acid) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Mathematics. --- Bioinformatics. --- Operations research. --- Management science. --- Probabilities. --- Statistics. --- Quality control. --- Reliability. --- Industrial safety. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Quality Control, Reliability, Safety and Risk. --- Operations Research, Management Science. --- Stochastic processes --- Deoxyribose --- Nucleic acids --- Genes --- Distribution (Probability theory. --- Mathematical statistics. --- System safety. --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Systems engineering --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Data processing --- Prevention --- Statistics . --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Standardization --- Quality assurance --- Quality of products --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk