Pierre Bremaud's Books

Markov Chains

Gibbs Fields, Monte Carlo Simulation and Queues

By: Pierre Brémaud

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Markov Chains

Gibbs Fields, Monte Carlo Simulation and Queues

By: Pierre Brémaud

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

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Page Count

564

Publisher

Springer Nature

Published Date

ISBN 10

3030459829

ISBN 13

9783030459826

Point Process Calculus in Time and Space

An Introduction with Applications

By: Pierre Brémaud

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Point Process Calculus in Time and Space

An Introduction with Applications

By: Pierre Brémaud

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

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Page Count

556

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Springer Nature

Published Date

ISBN 10

3030627535

ISBN 13

9783030627539

Probability Theory and Stochastic Processes

By: Pierre Brémaud

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Probability Theory and Stochastic Processes

By: Pierre Brémaud

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.

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Page Count

717

Publisher

Springer Nature

Published Date

ISBN 10

3030401839

ISBN 13

9783030401832

Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

By: Pierre Brémaud

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Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

By: Pierre Brémaud

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

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Page Count

561

Publisher

Springer

Published Date

ISBN 10

3319434764

ISBN 13

9783319434766

Fourier Analysis and Stochastic Processes

By: Pierre Brémaud

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Fourier Analysis and Stochastic Processes

By: Pierre Brémaud

This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.

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Page Count

396

Publisher

Springer

Published Date

ISBN 10

3319095900

ISBN 13

9783319095905

Elements of Queueing Theory

Palm Martingale Calculus and Stochastic Recurrences

By: Francois Baccelli,Pierre Bremaud

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Elements of Queueing Theory

Palm Martingale Calculus and Stochastic Recurrences

By: Francois Baccelli,Pierre Bremaud

This fundamental exposition of queueing theory, written by leading researchers, answers the need for a mathematically sound reference work on the subject and has become the standard reference. The thoroughly revised second edition contains a substantial number of exercises and their solutions, which makes the book suitable as a textbook.

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Page Count

346

Publisher

Springer Science & Business Media

Published Date

ISBN 10

366211657X

ISBN 13

9783662116579

An Introduction to Probabilistic Modeling

By: Pierre Bremaud

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An Introduction to Probabilistic Modeling

By: Pierre Bremaud

Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

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Page Count

222

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Springer Science & Business Media

Published Date

ISBN 10

1461210461

ISBN 13

9781461210467

An Introduction to Applied Probability

By: Pierre Brémaud

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An Introduction to Applied Probability

By: Pierre Brémaud

This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences. The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above. The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for the efficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models: Markov chains, which are omnipresent and versatile models in applied probability Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks Brownian motion, which models fluctuations in the stock market and the "white noise" of physics Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences. This book can be used as a text in various ways and at different levels of study. Essentially, it provides the material for a two-semester graduate course on probability and stochastic processes in a department of applied mathematics or for students in departments where stochastic models play an essential role. The progressive introduction of concepts and tools, along with the inclusion of numerous examples, also makes this book well-adapted for self-study.

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Page Count

498

Publisher

Springer Nature

Published Date

ISBN 10

3031493060

ISBN 13

9783031493065

Mathematical Principles of Signal Processing

Fourier and Wavelet Analysis

By: Pierre Bremaud

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Mathematical Principles of Signal Processing

Fourier and Wavelet Analysis

By: Pierre Bremaud

From the reviews: "[...] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews

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Page Count

263

Publisher

Springer Science & Business Media

Published Date

ISBN 10

147573669X

ISBN 13

9781475736694

Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

By: Pierre Bremaud

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Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

By: Pierre Bremaud

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Page Count

456

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Springer Science & Business Media

Published Date

ISBN 10

1475731248

ISBN 13

9781475731248

Markov Chains

Gibbs Fields, Monte Carlo Simulation and Queues

By: Pierre Brémaud

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Markov Chains

Gibbs Fields, Monte Carlo Simulation and Queues

By: Pierre Brémaud

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Page Count

564

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Springer Nature

Published Date

ISBN 10

3030459829

ISBN 13

9783030459826

Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

By: Pierre Brémaud

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Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

By: Pierre Brémaud

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Page Count

561

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Springer

Published Date

ISBN 10

3319434764

ISBN 13

9783319434766

Fourier Analysis and Stochastic Processes

By: Pierre Brémaud

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Fourier Analysis and Stochastic Processes

By: Pierre Brémaud

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Page Count

396

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Springer

Published Date

ISBN 10

3319095900

ISBN 13

9783319095905

Probability Theory and Stochastic Processes

By: Pierre Brémaud

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Probability Theory and Stochastic Processes

By: Pierre Brémaud

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Page Count

717

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Springer Nature

Published Date

ISBN 10

3030401839

ISBN 13

9783030401832

Point Process Calculus in Time and Space

An Introduction with Applications

By: Pierre Brémaud

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Point Process Calculus in Time and Space

An Introduction with Applications

By: Pierre Brémaud

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Page Count

556

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Springer Nature

Published Date

ISBN 10

3030627535

ISBN 13

9783030627539

Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

By: Pierre Bremaud

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Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

By: Pierre Bremaud

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Page Count

456

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475731248

ISBN 13

9781475731248

An Introduction to Probabilistic Modeling

By: Pierre Bremaud

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An Introduction to Probabilistic Modeling

By: Pierre Bremaud

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222

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Springer Science & Business Media

Published Date

ISBN 10

1461210461

ISBN 13

9781461210467

Point Processes and Queues, Martingale Dynamics

By: Pierre Brémaud

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Point Processes and Queues, Martingale Dynamics

By: Pierre Brémaud

From the Introduction: " The emphasis has been placed on topics of interest in systems science at large...The level of exposition and the inclusion of a large number of exercises with complete detailed solutions make this book usable as a text for graduate students in applied probability, electrical engineering, computer science, and operations research. The prerequisites in probability and random processes are recalled in the Appendices.

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