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Author: Zhenting Hou
Publisher: Springer Science & Business Media
ISBN: 3642681271
Category : Mathematics
Languages : en
Pages : 286
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Book Description
Markov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes.
Author: Zhenting Hou
Publisher: Springer Science & Business Media
ISBN: 3642681271
Category : Mathematics
Languages : en
Pages : 286
Get Book Here
Book Description
Markov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes.
Author: Chen-Ting Hou
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Xiangqun Yang
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Reaches the forefront of research in the construction theory of denumerable Markov processes and gives impetus to the development of probability theory. Introduces Markov processes and their construction; surveys research in the field; and presents the author's original results, which include complete solutions to some important problems, many published here for the first time in English. Complete solutions are given for two key construction problems: birth-death processes and two-sided birth-death processes.
Author: Wolfgang Woess
Publisher: Bradt Travel Guides
ISBN: 9783037190715
Category : Mathematics
Languages : en
Pages : 380
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Book Description
Markov chains are among the basic and most important examples of random processes. This book is about time-homogeneous Markov chains that evolve with discrete time steps on a countable state space. A specific feature is the systematic use, on a relatively elementary level, of generating functions associated with transition probabilities for analyzing Markov chains. Basic definitions and facts include the construction of the trajectory space and are followed by ample material concerning recurrence and transience, the convergence and ergodic theorems for positive recurrent chains. There is a side-trip to the Perron-Frobenius theorem. Special attention is given to reversible Markov chains and to basic mathematical models of population evolution such as birth-and-death chains, Galton-Watson process and branching Markov chains. A good part of the second half is devoted to the introduction of the basic language and elements of the potential theory of transient Markov chains. Here the construction and properties of the Martin boundary for describing positive harmonic functions are crucial. In the long final chapter on nearest neighbor random walks on (typically infinite) trees the reader can harvest from the seed of methods laid out so far, in order to obtain a rather detailed understanding of a specific, broad class of Markov chains. The level varies from basic to more advanced, addressing an audience from master's degree students to researchers in mathematics, and persons who want to teach the subject on a medium or advanced level. Measure theory is not avoided; careful and complete proofs are provided. A specific characteristic of the book is the rich source of classroom-tested exercises with solutions.
Author: John G. Kemeny
Publisher: Springer Science & Business Media
ISBN: 1468494554
Category : Mathematics
Languages : en
Pages : 495
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Book Description
With the first edition out of print, we decided to arrange for republi cation of Denumerrible Markov Ohains with additional bibliographic material. The new edition contains a section Additional Notes that indicates some of the developments in Markov chain theory over the last ten years. As in the first edition and for the same reasons, we have resisted the temptation to follow the theory in directions that deal with uncountable state spaces or continuous time. A section entitled Additional References complements the Additional Notes. J. W. Pitman pointed out an error in Theorem 9-53 of the first edition, which we have corrected. More detail about the correction appears in the Additional Notes. Aside from this change, we have left intact the text of the first eleven chapters. The second edition contains a twelfth chapter, written by David Griffeath, on Markov random fields. We are grateful to Ted Cox for his help in preparing this material. Notes for the chapter appear in the section Additional Notes. J.G.K., J.L.S., A.W.K.
Author: Marius Iosifescu
Publisher: Courier Corporation
ISBN: 0486150585
Category : Mathematics
Languages : en
Pages : 305
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Book Description
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models. The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic chains. A complete study of the general properties of homogeneous chains follows. Succeeding chapters examine the fundamental role of homogeneous infinite Markov chains in mathematical modeling employed in the fields of psychology and genetics; the basics of nonhomogeneous finite Markov chain theory; and a study of Markovian dependence in continuous time, which constitutes an elementary introduction to the study of continuous parameter stochastic processes.
Author: Zhenting Hou
Publisher: Springer Science & Business Media
ISBN: 146130265X
Category : Mathematics
Languages : en
Pages : 501
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Book Description
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.
Author: John G. Kemeny
Publisher:
ISBN: 9787506200707
Category : Markov processes
Languages : en
Pages : 484
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Book Description
Author: K. L. Chung
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 80
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Book Description
Author: Antonio Pacheco
Publisher: World Scientific
ISBN: 9814471704
Category : Mathematics
Languages : en
Pages : 237
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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.
