Semi Markov Processes
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Semi Markov Processes And Reliability
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Author : Nikolaos Limnios
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-16
Semi Markov Processes And Reliability written by Nikolaos Limnios and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-16 with Technology & Engineering categories.
At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.
Applied Semi Markov Processes
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Author : Jacques Janssen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-08
Applied Semi Markov Processes written by Jacques Janssen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-08 with Mathematics categories.
Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems. The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes. Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.
Semi Markov Models And Applications
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Author : Jacques Janssen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Semi Markov Models And Applications written by Jacques Janssen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This book presents a selection of papers presented to the Second Inter national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applications in Reliability and Maintenance, Biomedicine, Queue ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic models can be applied to financial and insur ance models as we have to evaluate the uncertainty of the future market behavior in order, firstly, to propose different measures for important risks such as the interest risk, the risk of default or the risk of catas trophe and secondly, to describe how to act in order to optimize the situation in time. Recently, the concept of VaR (Value at Risk) was "discovered" in portfolio theory enlarging so the fundamental model of Markowitz.
Semi Markov Models
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Author : Jacques Janssen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Semi Markov Models written by Jacques Janssen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
Semi Markov Processes
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Author : Franciszek Grabski
language : en
Publisher: Elsevier
Release Date : 2014-09-25
Semi Markov Processes written by Franciszek Grabski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-25 with Mathematics categories.
Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. - Clearly defines the properties and theorems from discrete state Semi-Markov Process (SMP) theory - Describes the method behind constructing Semi-Markov (SM) models and SM decision models in the field of reliability and maintenance - Provides numerous individual versions of SM models, including the most recent and their impact on system reliability and maintenance
Nonlinearly Perturbed Semi Markov Processes
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Author : Dmitrii Silvestrov
language : en
Publisher: Springer
Release Date : 2017-09-06
Nonlinearly Perturbed Semi Markov Processes written by Dmitrii Silvestrov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.
Semi Markov Processes And Reliability
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Author : Nikolaos Limnios
language : en
Publisher:
Release Date : 2001
Semi Markov Processes And Reliability written by Nikolaos Limnios and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Markov processes categories.
Continuous Semi Markov Processes
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Author : Boris Harlamov
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-01
Continuous Semi Markov Processes written by Boris Harlamov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.
This title considers the special of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times. The class of semi-Markov processes includes strong Markov processes, Lévy and Smith stepped semi-Markov processes, and some other subclasses. Extensive coverage is devoted to non-Markovian semi-Markov processes with continuous trajectories and, in particular, to semi-Markov diffusion processes. Readers looking to enrich their knowledge on Markov processes will find this book a valuable resource.
Semi Markov Risk Models For Finance Insurance And Reliability
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Author : Jacques Janssen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-15
Semi Markov Risk Models For Finance Insurance And Reliability written by Jacques Janssen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-15 with Mathematics categories.
This book aims to give a complete and self-contained presentation of semi- Markov models with finitely many states, in view of solving real life problems of risk management in three main fields: Finance, Insurance and Reliability providing a useful complement to our first book (Janssen and Manca (2006)) which gives a theoretical presentation of semi-Markov theory. However, to help assure the book is self-contained, the first three chapters provide a summary of the basic tools on semi-Markov theory that the reader will need to understand our presentation. For more details, we refer the reader to our first book (Janssen and Manca (2006)) whose notations, definitions and results have been used in these four first chapters. Nowadays, the potential for theoretical models to be used on real-life problems is severely limited if there are no good computer programs to process the relevant data. We therefore systematically propose the basic algorithms so that effective numerical results can be obtained. Another important feature of this book is its presentation of both homogeneous and non-homogeneous models. It is well known that the fundamental structure of many real-life problems is n- homogeneous in time, and the application of homogeneous models to such problems gives, in the best case, only approximated results or, in the worst case, nonsense results.
Perturbed Semi Markov Type Processes I
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Author : Dmitrii Silvestrov
language : en
Publisher: Springer Nature
Release Date : 2022-03-25
Perturbed Semi Markov Type Processes I written by Dmitrii Silvestrov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-25 with Mathematics categories.
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.