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The Construction Theory Of Denumerable Markov Processes
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Book Synopsis The Construction Theory of Denumerable Markov Processes by : Xiangqun Yang
Download or read book The Construction Theory of Denumerable Markov Processes written by Xiangqun Yang and published by . This book was released on 1990-12-21 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Denumerable Markov Chains by : Wolfgang Woess
Download or read book Denumerable Markov Chains written by Wolfgang Woess and published by Bradt Travel Guides. This book was released on 2009 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Homogeneous Denumerable Markov Processes by : Zhenting Hou
Download or read book Homogeneous Denumerable Markov Processes written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Markov Processes by : E. B. Dynkin
Download or read book Theory of Markov Processes written by E. B. Dynkin and published by Elsevier. This book was released on 2014-05-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.
Book Synopsis Topics in the Constructive Theory of Countable Markov Chains by : G. Fayolle
Download or read book Topics in the Constructive Theory of Countable Markov Chains written by G. Fayolle and published by Cambridge University Press. This book was released on 1995-05-18 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides methods of analysing Markov chains based on Lyapunov functions.
Book Synopsis Denumerable Markov Chains by : John G. Kemeny
Download or read book Denumerable Markov Chains written by John G. Kemeny and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Markov Processes by : Evgenij Borisovic Dynkin
Download or read book Markov Processes written by Evgenij Borisovic Dynkin and published by Springer. This book was released on 2012-08-15 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.
Book Synopsis Markov Processes by : Stewart N. Ethier
Download or read book Markov Processes written by Stewart N. Ethier and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference." -American Scientist "There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook." -Journal of Statistical Physics Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.
Book Synopsis Markov Processes and Controlled Markov Chains by : Zhenting Hou
Download or read book Markov Processes and Controlled Markov Chains written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Labelled Markov Processes by : Prakash Panangaden
Download or read book Labelled Markov Processes written by Prakash Panangaden and published by Imperial College Press. This book was released on 2009 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Markov Chains written by D. Revuz and published by Elsevier. This book was released on 2008-07-15 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
Book Synopsis Analysis of Health Surveys by : Edward L. Korn
Download or read book Analysis of Health Surveys written by Edward L. Korn and published by John Wiley & Sons. This book was released on 2011-01-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to apply statistical methods to survey data--a guide toeffective analysis of health surveys. With large health surveys becoming increasingly available forpublic use, researchers with little experience in survey methodsare often faced with analyzing data from surveys to addressscientific and programmatic questions. This practical book providesstatistical techniques for use in survey analysis, making healthsurveys accessible to statisticians, biostatisticians,epidemiologists, and health researchers. The authors clearlyexplain the theory and methods of survey analysis along withreal-world applications. They draw on their work at the NationalInstitutes of Health as well as up-to-date information from acrossthe literature to present: * The sampling background necessary to understand health surveys. * The application of such techniques as t-tests, linear regression,logistic regression, and survival analysis to survey data. * The use of sample weights in survey data analysis. * Dealing with complications in variance estimation in large healthsurveys. * Applications involving cross-sectional, longitudinal, andmultiple cross-sectional surveys, and the use of surveys to performpopulation- based case-control analyses. * Guidance on the correct use of statistical methods found insoftware packages. * Extensive bibliography.
Book Synopsis Fourier Analysis of Time Series by : Peter Bloomfield
Download or read book Fourier Analysis of Time Series written by Peter Bloomfield and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition: * Devotes an entire chapter to complex demodulation * Treats harmonic regression in two separate chapters * Features a more succinct discussion of the fast Fourier transform * Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility * Includes Web addresses for all time series data used in the examples An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.
Book Synopsis Fractional Factorial Plans by : Aloke Dey
Download or read book Fractional Factorial Plans written by Aloke Dey and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop reference to fractional factorials and relatedorthogonal arrays. Presenting one of the most dynamic areas of statistical research,this book offers a systematic, rigorous, and up-to-date treatmentof fractional factorial designs and related combinatorialmathematics. Leading statisticians Aloke Dey and Rahul Mukerjeeconsolidate vast amounts of material from the professionalliterature--expertly weaving fractional replication, orthogonalarrays, and optimality aspects. They develop the basic theory offractional factorials using the calculus of factorial arrangements,thereby providing a unified approach to the study of fractionalfactorial plans. An indispensable guide for statisticians inresearch and industry as well as for graduate students, FractionalFactorial Plans features: * Construction procedures of symmetric and asymmetric orthogonalarrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based onorthogonal arrays. * Trend-free plans, minimum aberration plans, and search andsupersaturated designs. * Numerous examples and extensive references.
Download or read book Geostatistics written by Jean-Paul Chilès and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel, practical approach to modeling spatial uncertainty. This book deals with statistical models used to describe natural variables distributed in space or in time and space. It takes a practical, unified approach to geostatistics-integrating statistical data with physical equations and geological concepts while stressing the importance of an objective description based on empirical evidence. This unique approach facilitates realistic modeling that accounts for the complexity of natural phenomena and helps solve economic and development problems-in mining, oil exploration, environmental engineering, and other real-world situations involving spatial uncertainty. Up-to-date, comprehensive, and well-written, Geostatistics: Modeling Spatial Uncertainty explains both theory and applications, covers many useful topics, and offers a wealth of new insights for nonstatisticians and seasoned professionals alike. This volume: * Reviews the most up-to-date geostatistical methods and the types of problems they address. * Emphasizes the statistical methodologies employed in spatial estimation. * Presents simulation techniques and digital models of uncertainty. * Features more than 150 figures and many concrete examples throughout the text. * Includes extensive footnoting as well as a thorough bibliography. Geostatistics: Modeling Spatial Uncertainty is the only geostatistical book to address a broad audience in both industry and academia. An invaluable resource for geostatisticians, physicists, mining engineers, and earth science professionals such as petroleum geologists, geophysicists, and hydrogeologists, it is also an excellent supplementary text for graduate-level courses in related subjects.
Book Synopsis Statistical Modeling by Wavelets by : Brani Vidakovic
Download or read book Statistical Modeling by Wavelets written by Brani Vidakovic and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.
Book Synopsis Applied Regression Including Computing and Graphics by : R. Dennis Cook
Download or read book Applied Regression Including Computing and Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step guide to computing and graphics in regression analysis In this unique book, leading statisticians Dennis Cook and Sanford Weisberg expertly blend regression fundamentals and cutting-edge graphical techniques. They combine and up- date most of the material from their widely used earlier work, An Introduction to Regression Graphics, and Weisberg's Applied Linear Regression; incorporate the latest in statistical graphics, computing, and regression models; and wind up with a modern, fully integrated approach to one of the most important tools of data analysis. In 23 concise, easy-to-digest chapters, the authors present:? A wealth of simple 2D and 3D graphical techniques, helping visualize results through graphs * An improved version of the user-friendly Arc software, which lets readers promptly implement new ideas * Complete coverage of regression models, including logistic regression and generalized linear models * More than 300 figures, easily reproducible on the computer * Numerous examples and problems based on real data * A companion Web site featuring free software and advice, available at www.wiley.com/mathem atics Accessible, self-contained, and fully referenced, Applied Regression Including Computing and Graphics assumes only a first course in basic statistical methods and provides a bona fide user manual for the Arc software. It is an invaluable resource for anyone interested in learning how to analyze regression problems with confidence and depth.
