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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. .

Mathematics. --- Computer communication systems. --- Coding theory. --- Mathematical statistics. --- Probabilities. --- Graph theory. --- Probability Theory and Stochastic Processes. --- Probability and Statistics in Computer Science. --- Graph Theory. --- Coding and Information Theory. --- Computer Communication Networks. --- Probability --- Statistical inference --- Mathematics --- Statistics, Mathematical --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Math --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Statistical methods --- Extremal problems --- Distribution (Probability theory. --- Computer science. --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Informatics --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Data processing. --- Information theory. --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Communication theory --- Communication --- Cybernetics --- Combinatorial analysis --- Topology --- Statistics --- Sampling (Statistics) --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Distributed processing --- Computer science --- Computer networks. --- Probability Theory. --- Computer mathematics

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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). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spaces in the first chapter) make the book self-contained. 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.

Fourier analysis. --- Mathematics. --- Distribution (Probability theory) --- Probability Theory and Stochastic Processes. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Analysis, Fourier --- Math --- Distribution functions --- Frequency distribution --- Probabilities. --- Fourier Analysis. --- Fourier Analysis --- Distribution (Probability theory). --- Mathématiques --- Analyse de Fourier --- Distribution (Théorie des probabilités) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Distribution (Probability theory. --- Mathematical analysis --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This 2nd edition is a thoroughly revised and augmented version of the book with the same title published in 1999. The author begins with the elementary theory of Markov chains and very progressively brings the reader to more advanced topics. He gives a useful review of probability, making the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics is slowly and carefully developed, in order to make self-study easier. The book treats the classical topics of Markov chain theory, both in discrete time and continuous time, as well as connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete-time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The main additions of the 2nd edition are the exact sampling algorithm of Propp and Wilson, the electrical network analogy of symmetric random walks on graphs, mixing times and additional details on the branching process. The structure of the book has been modified in order to smoothly incorporate this new material. Among the features that should improve reader-friendliness, the three main ones are: a shared numbering system for the definitions, theorems and examples; the attribution of titles to the examples and exercises; and the blue highlighting of important terms. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.

Markov processes. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Probabilities. --- Operations research. --- Decision making. --- Electrical engineering. --- Probability Theory and Stochastic Processes. --- Operations Research/Decision Theory. --- Electrical Engineering. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Electric engineering --- Engineering --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making

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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.

Probabilities. --- Fourier analysis. --- Probability Theory and Stochastic Processes. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Point processes. --- Processes, Point --- Stochastic processes

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Statistical science --- Operational research. Game theory --- stochastische analyse --- kansrekening --- statistisch onderzoek