Stationary Processes and Discrete Parameter Markov Processes / Graduate Texts in Mathematics Bd.293 (PDF)
Aktionspreis bis 30.06.2024*
*befristete Preissenkung des Verlages
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenloser tolino webreader
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.
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.
- Autoren: Rabi Bhattacharya , Edward C. Waymire
- 2022, 1st ed. 2022, 449 Seiten, Englisch
- Verlag: Springer International Publishing
- ISBN-10: 3031009436
- ISBN-13: 9783031009433
- Erscheinungsdatum: 01.12.2022
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 4.72 MB
- Ohne Kopierschutz
- Vorlesefunktion
Schreiben Sie einen Kommentar zu "Stationary Processes and Discrete Parameter Markov Processes / Graduate Texts in Mathematics Bd.293".
Kommentar verfassen