Markov Chains

Author: J. R. Norris

Publisher: Cambridge University Press

ISBN: 9780521633963

Category: Mathematics

Page: 237

View: 5063

In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.
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Wahrscheinlichkeitstheorie

Author: Achim Klenke

Publisher: Springer-Verlag

ISBN: 3642360181

Category: Mathematics

Page: 650

View: 4072

Seit seinem Erscheinen hat sich das Buch umgehend als Standardwerk für eine umfassende und moderne Einführung in die Wahrscheinlichkeitstheorie und ihre maßtheoretischen Grundlagen etabliert. Themenschwerpunkte sind: Maß- und Integrationstheorie, Grenzwertsätze für Summen von Zufallsvariablen (Gesetze der Großen Zahl, Zentraler Grenzwertsatz, Ergodensätze, Gesetz vom iterierten Logarithmus, Invarianzprinzipien, unbegrenzt teilbare Verteilungen), Martingale, Perkolation, Markovketten und elektrische Netzwerke, Konstruktion stochastischer Prozesse, Poisson'scher Punktprozess, Brown'sche Bewegung, stochastisches Integral und stochastische Differentialgleichungen. Bei der Bearbeitung der Neuauflage wurde viel Wert auf eine noch zugänglichere didaktische Aufbereitung des Textes gelegt, und es wurden viele neue Abbildungen sowie Textergänzungen hinzugefügt.
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Introduction to Markov Chains

With Special Emphasis on Rapid Mixing

Author: Ehrhard Behrends

Publisher: Vieweg+Teubner Verlag

ISBN: 3322901572

Category: Mathematics

Page: 234

View: 6620

Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.
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Understanding Markov Chains

Examples and Applications

Author: Nicolas Privault

Publisher: Springer

ISBN: 9811306591

Category: Mathematics

Page: 372

View: 8908

This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
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Markov Chains and Mixing Times: Second Edition

Author: David A. Levin,Yuval Peres

Publisher: American Mathematical Soc.

ISBN: 1470429624

Category: Distribution (Probability theory)

Page: 447

View: 5965

This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.
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Statistical Models

Author: A. C. Davison

Publisher: Cambridge University Press

ISBN: 1139437410

Category: Mathematics

Page: N.A

View: 2961

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.
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An Introduction to Stochastic Processes with Applications to Biology

Author: Linda J. S. Allen

Publisher: Prentice Hall

ISBN: 9780130352187

Category: Mathematics

Page: 385

View: 9182

Plenty of examples, diagrams, and figures take readers step-by-step through well-known classical biological models to ensure complete understanding of stochastic formulation. Probability, Markov Chains, discrete time branching processes, population genetics, and birth and death chains. For biologists and other professionals who want a comprehensive, easy-to-follow introduction to stochastic formulation as it pertains to biology.
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Probability

Theory and Examples

Author: Rick Durrett

Publisher: Cambridge University Press

ISBN: 113949113X

Category: Mathematics

Page: N.A

View: 3356

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
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Mathematische Statistik

Author: Bartel L. van der Waerden

Publisher: Springer-Verlag

ISBN: 3642649742

Category: Mathematics

Page: 360

View: 2041

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Statistical Analysis of Stochastic Processes in Time

Author: J. K. Lindsey

Publisher: Cambridge University Press

ISBN: 9781139454513

Category: Mathematics

Page: 338

View: 5028

This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
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Measure Theory and Filtering

Introduction and Applications

Author: Lakhdar Aggoun,Robert J. Elliott

Publisher: Cambridge University Press

ISBN: 9781139456241

Category: Mathematics

Page: N.A

View: 2781

This book was published in 2004. The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers.
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Understanding Probability

Author: Henk Tijms

Publisher: Cambridge University Press

ISBN: 110765856X

Category: Mathematics

Page: 562

View: 3883

Using everyday examples to demystify probability, this classic is now in its third edition with new chapters, exercises and examples.
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Grundbegriffe der Wahrscheinlichkeitsrechnung

Author: A. Kolomogoroff

Publisher: Springer-Verlag

ISBN: 3642498884

Category: Mathematics

Page: 62

View: 6164

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Quantitative Methoden in den Wirtschaftswissenschaften

Hans Paul Künzi zum 65. Geburtstag

Author: Peter Kall,Juerg Kohlas,Werner Popp,Carl-August Zehnder

Publisher: Springer-Verlag

ISBN: 3642743064

Category: Business & Economics

Page: 240

View: 2611

Anläßlich des 65. Geburtstages von Hans Paul Künzi haben sich Weggefährten, Mitarbeiter und Schüler aus den Jahren seines Wirkens als Hochschullehrer zusammengetan, um wenigstens punktuell aufzu zeigen, wie und wohin in den letzten zwei Jahrzehnten verschiedene theoretische und empirische Entwicklungen verlaufen sind, die der Jubilar zumindest in der Schweiz und zu einem guten Teil auch darüber hinaus mitaufgebaut und in den Anfängen beeinflußt hat. Zu diesem Vorhaben fanden die Herausgeber vielseitige Unterstützung. Zunächst von den beteiligten Autoren, die mit spontanen Zusagen und in vorbildlicher Weise ihre Beiträge termingerecht fertiggestellt haben. Darüber hinaus hat ein größerer Kreis von Persönlichkeiten mit Rat und Tat die Entstehung der Schrift gefördert, wobei besonders auch auf ein großes Entgegenkommen des Springer-Verlages zu verweisen ist. Allen möchten wir für die Hilfe aufrichtig danken. Angesichts der Tatsache, daß Hans Paul Künzi bereits vor fast zwei Jahrzehnten seine wissenschaftliche Laufbahn zugunsten einer anderen Verpflichtung aufgegeben hat, liegt die Frage nahe, warum wir -nach wie vor der akademischen Welt verbunden -heute noch von der Persönlichkeit Künzi beeindruckt sind. Dazu sei kurz auf sein damaliges Wirken als Professor an der Universität Zürich und an der ETH Zürich zurückgeblendet.
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Statistical Pronunciation Modeling for Non-Native Speech Processing

Author: Rainer E. Gruhn,Wolfgang Minker,Satoshi Nakamura

Publisher: Springer Science & Business Media

ISBN: 9783642195860

Category: Technology & Engineering

Page: 114

View: 8740

In this work, the authors present a fully statistical approach to model non--native speakers' pronunciation. Second-language speakers pronounce words in multiple different ways compared to the native speakers. Those deviations, may it be phoneme substitutions, deletions or insertions, can be modelled automatically with the new method presented here. The methods is based on a discrete hidden Markov model as a word pronunciation model, initialized on a standard pronunciation dictionary. The implementation and functionality of the methodology has been proven and verified with a test set of non-native English in the regarding accent. The book is written for researchers with a professional interest in phonetics and automatic speech and speaker recognition.
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Kalman-Bucy-Filter

determinist. Beobachtung u. stochast. Filterung

Author: Karl Brammer,Gerhard Siffling

Publisher: N.A

ISBN: N.A

Category: Control theory

Page: 232

View: 695

Das Buch will die mannigfaltigen Aufgaben der heutigen Regelungs- und Steuerungstechnik und ihre Lösung nahebringen. Das soll mit möglichst geringem Zeit- und Arbeitsaufwand für den Leser verbunden sein. Leichte Verständlichkeit, Anschaulichkeit und Anwendungsnähe sind deshalb Hauptgesichtspunkt der Darstellung. Vollständigkeit ist nicht angestrebt, vielmehr Darstellung des Wesentlichen. Mathematische Methoden werden auf das Notwendige beschränkt.
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Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung

Publisher: Springer-Verlag

ISBN: 3642670334

Category: Mathematics

Page: 346

View: 3521

Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1
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Internationale mathematische Nachrichten

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7721

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
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