Author: Murray Rosenblatt
Publisher: Springer Science & Business Media
ISBN: 3642652387
Category : Mathematics
Languages : en
Pages : 282
Book Description
This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting course on Markov processes or stationary processes. For the most part these questions are considered for discrete parameter processes, although they are also of obvious interest for continuous time parameter processes. This allows one to avoid the delicate measure theoretic questions that might arise in the continuous parameter case. There is an attempt to motivate the material in terms of applications. Many of the topics concern general questions of structure and representation of processes that have not previously been presented in book form. A set of notes comment on the many problems that are still left open and related material in the literature. It is also hoped that the book will be useful as a reference to the reader who would like an introduction to these topics as well as to the reader interested in extending and completing results of this type.
Markov Processes, Structure and Asymptotic Behavior
Author: Murray Rosenblatt
Publisher: Springer Science & Business Media
ISBN: 3642652387
Category : Mathematics
Languages : en
Pages : 282
Book Description
This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting course on Markov processes or stationary processes. For the most part these questions are considered for discrete parameter processes, although they are also of obvious interest for continuous time parameter processes. This allows one to avoid the delicate measure theoretic questions that might arise in the continuous parameter case. There is an attempt to motivate the material in terms of applications. Many of the topics concern general questions of structure and representation of processes that have not previously been presented in book form. A set of notes comment on the many problems that are still left open and related material in the literature. It is also hoped that the book will be useful as a reference to the reader who would like an introduction to these topics as well as to the reader interested in extending and completing results of this type.
Publisher: Springer Science & Business Media
ISBN: 3642652387
Category : Mathematics
Languages : en
Pages : 282
Book Description
This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting course on Markov processes or stationary processes. For the most part these questions are considered for discrete parameter processes, although they are also of obvious interest for continuous time parameter processes. This allows one to avoid the delicate measure theoretic questions that might arise in the continuous parameter case. There is an attempt to motivate the material in terms of applications. Many of the topics concern general questions of structure and representation of processes that have not previously been presented in book form. A set of notes comment on the many problems that are still left open and related material in the literature. It is also hoped that the book will be useful as a reference to the reader who would like an introduction to these topics as well as to the reader interested in extending and completing results of this type.
Markov processes
Markov Processes for Stochastic Modeling
Author: Masaaki Kijima
Publisher: CRC Press
ISBN: 9780412606601
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book presents an algebraic development of the theory of countable state space Markov chains with discrete and continuous time parameters.
Publisher: CRC Press
ISBN: 9780412606601
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book presents an algebraic development of the theory of countable state space Markov chains with discrete and continuous time parameters.
Markov Processes
Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Category : Mathematics
Languages : en
Pages : 600
Book Description
Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Category : Mathematics
Languages : en
Pages : 600
Book Description
Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.
Analysis of Markov Chain Models of Adaptive Processes
Author: K. R. Kaplan
Publisher:
ISBN:
Category : Adaptation (Physiology)
Languages : en
Pages : 116
Book Description
Learning and adaptation are considered to be stochastic in nature by most modern psychologists and by many engineers. Markov chains are among the simplest and best understood models of stochastic processes and, in recent years, have frequently found application as models of adaptive processes. A number of new techniques are developed for the analysis of synchronous and asynchronous Markov chains, with emphasis on the problems encountered in the use of these chains as models of adaptive processes. Signal flow analysis yields simplified computations of asymptotic success probabilities, delay times, and other indices of performance. The techniques are illustrated by several examples of adaptive processes. These examples yield further insight into the relations between adaptation and feedback. (Author).
Publisher:
ISBN:
Category : Adaptation (Physiology)
Languages : en
Pages : 116
Book Description
Learning and adaptation are considered to be stochastic in nature by most modern psychologists and by many engineers. Markov chains are among the simplest and best understood models of stochastic processes and, in recent years, have frequently found application as models of adaptive processes. A number of new techniques are developed for the analysis of synchronous and asynchronous Markov chains, with emphasis on the problems encountered in the use of these chains as models of adaptive processes. Signal flow analysis yields simplified computations of asymptotic success probabilities, delay times, and other indices of performance. The techniques are illustrated by several examples of adaptive processes. These examples yield further insight into the relations between adaptation and feedback. (Author).
Markov-modulated Processes And Semiregenerative Phenomena
Author: Antonio Pacheco
Publisher: World Scientific
ISBN: 9814471704
Category : Mathematics
Languages : en
Pages : 237
Book Description
The book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.
Publisher: World Scientific
ISBN: 9814471704
Category : Mathematics
Languages : en
Pages : 237
Book Description
The book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.
Continuous-Time Markov Chains and Applications
Author: George G. Yin
Publisher: Springer
ISBN: 1461206278
Category : Mathematics
Languages : en
Pages : 358
Book Description
Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.
Publisher: Springer
ISBN: 1461206278
Category : Mathematics
Languages : en
Pages : 358
Book Description
Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.
Change of Time Scale for Markov Processes
Author: Steven Orey
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 44
Book Description
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 44
Book Description
Labelled Markov Processes
Author: Prakash Panangaden
Publisher: Imperial College Press
ISBN: 1848162898
Category : Mathematics
Languages : en
Pages : 212
Book Description
Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs.
Publisher: Imperial College Press
ISBN: 1848162898
Category : Mathematics
Languages : en
Pages : 212
Book Description
Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs.
Nonlinearly Perturbed Semi-Markov Processes
Author: Dmitrii Silvestrov
Publisher: Springer
ISBN: 3319609882
Category : Mathematics
Languages : en
Pages : 151
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.
Publisher: Springer
ISBN: 3319609882
Category : Mathematics
Languages : en
Pages : 151
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.