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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Stationary Processes and Discrete Parameter Markov Processes
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Stationary Processes and Discrete Parameter Markov Processes
Rabi Bhattacharya, Edward C. Waymire (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.12.2022
Sprache
Englisch
EAN
9783031009419
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Rabi Bhattacharya, Edward C. Waymire
Seitenanzahl
449
Auflage
1
Einbandart
Gebundene Ausgabe
Schlagwörter
weakly stationary processes, discrete parameter Markov processes, spectral representation of a stationary process, Birkhoff’s Ergodic Theorem, discrete parameter Markov processes on a general state space, birth–death chains, hitting probabilities and absorption, large deviation theory for Markov processes, stationary ergodic Markov processes, geometric rates of convergence to equilibrium, applications of large deviation theory, Extended Perron-Frobenius Theorem, FKG inequalities, Kalman filter, stochastic processes textbook, advanced probability textbook
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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