This book is the result of the International Symposium on Semi� Markov Processes and their Applications held on June 4-7, 1984 at the Universite Libre de Bruxelles with the help of the FNRS (Fonds National de la Recherche Scientifique, Belgium), the Ministere de l'Education Nationale (Belgium) and the Bernoulli Society for Mathe� matical Statistics and Probability. This international meeting was planned to make a state of the art for the area of semi-Markov theory and its applications, to bring together researchers in this field and to create a platform for open and thorough discussion. Main themes of the Symposium are the first ten sections of this book. The last section presented here gives an exhaustive biblio� graphy on semi-Markov processes for the last ten years. Papers selected for this book are all invited papers and in addition some contributed papers retained after strong refereeing. Sections are I. Markov additive processes and regenerative systems II. Semi-Markov decision processes III. Algorithmic and computer-oriented approach IV. Semi-Markov models in economy and insurance V. Semi-Markov processes and reliability theory VI. Simulation and statistics for semi-Markov processes VII. Semi-Markov processes and queueing theory VIII. Branching IX. Applications in medicine X. Applications in other fields v PREFACE XI. A second bibliography on semi-Markov processes It is interesting to quote that sections IV to X represent a good sample of the main applications of semi-Markov processes i. e.

Contenuti

Section I. Markov Additive Processes and Regenerative Systems.- Some limit theorems for Markov additive processes.- Stationary regenerative processes.- Asymptotic analysis of some non-homogeneous semi-Markov processes.- Section II. Semi-Markov Decision Processes.- Markov and semi-Markov decision models and optimal stopping.- Markov decision drift processes.- The functional equations of undiscounted denumerable state Markov renewal programming.- Section III. Algorithmic and Computer-Oriented Approach.- Recursive moment formulas for regenerative simulation.- Computation of the state probabilities in a class of semi-regenerative queueing systems.- The superposition of two PH-renewal processes.- Section IV. Semi-Markov Models in Economy and Insurance.- Pension accumulation as a semi-Markov reward process, with applications to pension reform.- The structure of a firm’s optimal non-decreasing wage policy when recruitment is a wage dependent Poisson process.- Section V. Semi-Markov Processes and Reliability Theory.- Markov renewal processes in reliability analysis.- Deterioration processes.- Stochastic processes with an embedded point process and their application to system reliability analysis.- Section VI. Simulation and Statistics for Semi-Markov Processes.- Semi-Markov models for manpower planning.- Statistical analysis of semi-Markov processes based on the theory of counting processes.- Section VII. Semi-Markov Processes and Queueing Theory.- Approximation of stochastic models.- The method of renovating events and its applications in queueing theory.- On non-time homogeneity.- A semi-Markov queue vith exponential service times.- Section VIII. Branching.- Estimation theory for multitype branching processes.- Exact distribution of kin number in multitype Galton-Watson process.- Arbres de Galton-Watson.- Section IX. Applications in Medicine.- Some remarks on semi-Markov processes in medical statistics.- Semi-Markov and non-homogeneous Markov models in medicine.- Application of semi-Markov processes to health care planning: a model to study the flow of patients following the dialysis-transplantation plan.- Section X. Applications in Other Fields.- Applications of semi-Markov processes: a miscellany.- Social applications of semi-Markov processes.- Language modelling using a hidden Markov chain with application to automatic transcription of French stenotypy.- Semi-Markov processes in seismic risk analysis.- Section XI.- A second bibliography on semi-Markov processes.

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