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).

Zusammenfassung

Two important types of models for reliability and genetics, the semi-Markov and hidden semi-Markov models are presented in this book. Their importance relies on the fact that they generalize several previous models and provide new possibilities to handle real problems. For reliability scientists and engineers, this book comes with a new method for studying systems reliability and it offers modelling and estimation tools. As for the biologists, this work offers them a more adapted model for DNA analysis, namely the hidden semi-Markov model, which is more flexible than the hidden Markov models, extensively used in this field. Moreover, the hidden semi-Markov framework can be used in many other applications, such as reliability, signal treatment, speech or image processing, among others.

Inhalt
Discrete-Time Renewal Processes.- Semi-Markov Chains.- Non parametric Estimation for Semi-Markov Chains.- Reliability Theory for Discrete-Time Semi-Markov Systems.- Hidden Semi-Markov Model and Estimation.