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Semi Markov Processes and Reliability

Semi Markov Processes and Reliability Book
Author : N. Limnios,G. Oprisan
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461201616
Language : En, Es, Fr & De

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Book Description :

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.

Nonlinearly Perturbed Semi Markov Processes

Nonlinearly Perturbed Semi Markov Processes Book
Author : Dmitrii Silvestrov,Sergei Silvestrov
Publisher : Springer
Release : 2017-09-06
ISBN : 3319609882
Language : En, Es, Fr & De

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Book Description :

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 Models and Applications

Semi Markov Models and Applications Book
Author : Jacques Janssen,Nikolaos Limnios
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1461332885
Language : En, Es, Fr & De

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Book Description :

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 Chains and Hidden Semi Markov Models toward Applications

Semi Markov Chains and Hidden Semi Markov Models toward Applications Book
Author : Vlad Stefan Barbu,Nikolaos Limnios
Publisher : Springer
Release : 2008-08-28
ISBN : 9780387731711
Language : En, Es, Fr & De

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Book Description :

Here is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A 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.

Introduction to Hidden Semi Markov Models

Introduction to Hidden Semi Markov Models Book
Author : John Van der Hoek,Robert J. Elliott
Publisher : Cambridge University Press
Release : 2019
ISBN : 1108421601
Language : En, Es, Fr & De

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Book Description :

Develops the theory of Markov and semi-Markov processes in an elementary setting suitable for senior undergraduate and graduate students.

Semi Markov Risk Models for Finance Insurance and Reliability

Semi Markov Risk Models for Finance  Insurance and Reliability Book
Author : Jacques Janssen,Raimondo Manca
Publisher : Springer Science & Business Media
Release : 2007-05-15
ISBN : 0387707301
Language : En, Es, Fr & De

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Book Description :

Everyone working in related fields from applied mathematicians to statisticians to actuaries and operations researchers will find this a brilliantly useful practical text. The book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools.

Applied Semi Markov Processes

Applied Semi Markov Processes Book
Author : Jacques Janssen,Raimondo Manca
Publisher : Springer Science & Business Media
Release : 2006-02-08
ISBN : 0387295488
Language : En, Es, Fr & De

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Book Description :

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

Semi Markov Models Book
Author : Jacques Janssen
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 148990574X
Language : En, Es, Fr & De

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Book Description :

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.

AN APPROACH TO SEMI MARKOV PROCESSES

AN APPROACH TO SEMI MARKOV PROCESSES  Book
Author : Anonim
Publisher : Unknown
Release : 1970
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The paper reports on some of the mathematical results that the author obtained while seeking to refine Markov chain models. In an effort to take into account the waiting time in each state prior to transition, a non-Markov process was postulated. Subsequent investigation showed the process to be a reformulation of a semi-Markov process. In the present case, the equations for the flow resemble a multi-dimensional renewal process. The behavior of the system is described by a probability density which characterizes the process at any time t> 0, given that the states of the process were defined at time t = 0. It is shown in the special steady state case that the probability distribution yields results which are equivalent to those previously given.

Two Topics in Semi markov Processes 1 Semi markov Processes which are Functions of Markov Chains 2 Estimation of the Parameters of a Semi markov Process from Aggregate Data

Two Topics in Semi markov Processes   1  Semi markov Processes which are Functions of Markov Chains   2  Estimation of the Parameters of a Semi markov Process from Aggregate Data Book
Author : S. A. Shulman
Publisher : Unknown
Release : 1977
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Two Topics in Semi markov Processes 1 Semi markov Processes which are Functions of Markov Chains 2 Estimation of the Parameters of a Semi markov Process from Aggregate Data book written by S. A. Shulman, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Continuous Semi Markov Processes

Continuous Semi Markov Processes Book
Author : Boris Harlamov
Publisher : John Wiley & Sons
Release : 2013-03-01
ISBN : 111862405X
Language : En, Es, Fr & De

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Book Description :

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 Processes and Decision Making

Semi Markov Processes and Decision Making Book
Author : Mohamed A. H. Nasr
Publisher : Unknown
Release : 1976
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Semi Markov Processes and Decision Making book written by Mohamed A. H. Nasr, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Semi Markov Processes and Reliability

Semi Markov Processes and Reliability Book
Author : Nikolaos Limnios,Gheorghe Oprișan
Publisher : Unknown
Release : 2001
ISBN : 9783764341961
Language : En, Es, Fr & De

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Book Description :

Download Semi Markov Processes and Reliability book written by Nikolaos Limnios,Gheorghe Oprișan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Semi Markov Processes and Reliability

Semi Markov Processes and Reliability Book
Author : Nikolaos Limnios,G. Oprisan
Publisher : Birkhäuser
Release : 2011-09-26
ISBN : 9781461201625
Language : En, Es, Fr & De

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Book Description :

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

Applied Semi Markov Processes Book
Author : Jacques Janssen,Raimondo Manca
Publisher : Springer
Release : 2008-11-01
ISBN : 9780387510231
Language : En, Es, Fr & De

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Book Description :

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 Chains and Hidden Semi Markov Models toward Applications

Semi Markov Chains and Hidden Semi Markov Models toward Applications Book
Author : Vlad Stefan Barbu,Nikolaos Limnios
Publisher : Springer Science & Business Media
Release : 2009-01-07
ISBN : 0387731733
Language : En, Es, Fr & De

GET BOOK

Book Description :

Here is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A 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.

Markov Renewal and Piecewise Deterministic Processes

Markov Renewal and Piecewise Deterministic Processes Book
Author : Christiane Cocozza-Thivent
Publisher : Springer Nature
Release : 2021
ISBN : 3030704475
Language : En, Es, Fr & De

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Book Description :

This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.

Semi Markov Processes and Their Applications

Semi Markov Processes and Their Applications Book
Author : Dalice Audrey Sim
Publisher : Unknown
Release : 1975
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Semi Markov Processes and Their Applications book written by Dalice Audrey Sim, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Applications of Semi Markov Processes to Counter and Reliability Problems

Applications of Semi Markov Processes to Counter and Reliability Problems Book
Author : Richard E. Barlow,Stanford University. Applied Mathematics and Statistics Laboratory
Publisher : Unknown
Release : 1960
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Applications of Semi Markov Processes to Counter and Reliability Problems book written by Richard E. Barlow,Stanford University. Applied Mathematics and Statistics Laboratory, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Semi Markov Migration Models for Credit Risk

Semi Markov Migration Models for Credit Risk Book
Author : Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca
Publisher : John Wiley & Sons
Release : 2017-06-01
ISBN : 1119415128
Language : En, Es, Fr & De

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Book Description :

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules. This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.