Preface -- Contents -- Introduction -- Object of the Study -- The Underlying Idea in Semi-Markov Models -- Discrete Time -- Discrete-Time Semi-Markov Framework -- Discrete-Time Renewal Processes -- Semi-Markov Chains -- Semi-Markov Chain Estimation -- Reliability Theory of Discrete-Time Semi-Markov Systems -- Hidden Semi-Markov Models -- Discrete-Time Renewal Processes -- Renewal Chains -- Limit Theorems -- Delayed Renewal Chains -- Alternating Renewal Chain -- Exercises -- Semi-Markov Chains -- Markov Renewal Chains and Semi-Markov Chains -- Markov Renewal Theory -- Limit Theorems for Markov Renewal Chains -- Periodic SMC -- Monte Carlo Methods -- Example: a Textile Factory -- Exercises -- Nonparametric Estimation for Semi-Markov Chains -- Construction of the Estimators -- Asymptotic Properties of the Estimators -- Example: a Textile Factory (Continuation) -- Exercises -- Reliability Theory for Discrete-Time Semi-Markov Systems -- Reliability Function and Associated Measures -- Reliability -- Availability -- Maintainability -- Failure Rates -- Mean Hitting Times -- Nonparametric Estimation of Reliability -- Example: a Textile Factory (Continuation) -- Exercises -- Hidden Semi-Markov Model and Estimation -- Hidden Semi-Markov Model -- Estimation of a Hidden Semi-Markov Model -- Consistency of Maximum-Likelihood Estimator -- Asymptotic Normality of Maximum-Likelihood Estimator -- Monte Carlo Algorithm -- EM Algorithm for a Hidden Semi-Markov Model -- Preliminaries -- EM Algorithm for Hidden Model SM-M0 -- EM Algorithm for Hidden Model SM-M1 -- Proofs -- Example: CpG Island Detection -- Exercises -- Lemmas for Semi-Markov Chains -- Lemmas for Hidden Semi-Markov Chains -- Lemmas for Hidden SM-M0 Chains -- Lemmas for Hidden SM-M1 Chains -- Some Proofs -- Markov Chains -- Definition and Transition Function -- Strong Markov Property.

Recurrent and Transient States -- Stationary Distribution -- Markov Chains and Reliability -- Miscellaneous -- Notation -- References -- Index.