Stationary Processes and Discrete Parameter Markov Processes (Graduate Texts in Mathematics, 293)
Bhattacharya, Rabi; Waymire, Edward C.
ISBN 10: 303100941X ISBN 13: 9783031009419
Edité par Springer, 2022
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A propos de cet article
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Synopsis :
This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes.
À propos de l?auteur:
Rabi Bhattacharya is Professor of Mathematics at The University of Arizona. He is a Fellow of the Institute of Mathematical Statistics and a recipient of the U.S. Senior Scientist Humboldt Award and of a Guggenheim Fellowship. He has made significant contributions to the theory and application of Markov processes, and more recently, nonparametric statistical inference on manifolds. He has served on editorial boards of many international journals and has published several research monographs and graduate texts on probability and statistics.
Edward C. Waymire is Emeritus Professor of Mathematics at Oregon State University. He received a PhD in mathematics from the University of Arizona in the theory of interacting particle systems. His primary research concerns applications of probability and stochastic processes to problems of contemporary applied mathematics pertaining to various types of flows, dispersion, and random disorder. He is a former chief editor of the Annals of Applied Probability, and past president of the Bernoulli Society for Mathematical Statistics and Probability.
Both authors have co-authored numerous books, including A Basic Course in Probability Theory, which is an ideal companion to the current volume.
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Détails bibliographiques
Titre : Stationary Processes and Discrete Parameter ...
Éditeur : Springer
Date d'édition : 2022
Reliure : Couverture rigide
Etat : Neuf
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Stationary Processes and Discrete Parameter Markov Processes
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Springer International Publishing, 2022
ISBN 10 : 303100941X
ISBN 13 : 9783031009419
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Offers an in-depth study of stationary and discrete-time Markov processesBuilds from simple examples to formal proofs, illuminating key ideas and computationsExplores special topics that include applications of large deviation theory, coupl. N° de réf. du vendeur 571802070
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Stationary Processes and Discrete Parameter Markov Processes (Graduate Texts in Mathematics, 293) [Hardcover] Bhattacharya, Rabi and Waymire, Edward C.
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Buch. Etat : Neu. Stationary Processes and Discrete Parameter Markov Processes | Rabi Bhattacharya (u. a.) | Buch | xvii | Englisch | 2022 | Springer | EAN 9783031009419 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. N° de réf. du vendeur 121325564
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Springer International Publishing, 2022
ISBN 10 : 303100941X
ISBN 13 : 9783031009419
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study.After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff's Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth-death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter.Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed. N° de réf. du vendeur 9783031009419
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