Fourier Analysis and Stochastic Processes

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Pierre Brémaud graduated from the École Polytechnique and obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science at the University of California, Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference books and textbooks.

Zusammenfassung

Provides a self-contained mathematically rigorous introduction to the Fourier theory of functions, probability distributions and stochastic processes

Contains applications in signal processing and time series analysis

Includes a new treatment of power spectral measures of point processes and related stochastic processes

Includes supplementary material: [...]

Inhaltsverzeichnis

Fourier analysis of functions.- Fourier theory of probability distributions.- Fourier analysis of stochastic processes.- Fourier analysis of time series.- Power spectra of point processes.

Details

Erscheinungsjahr:	2014
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xiii 385 S. 2 s/w Illustr. 385 p. 2 illus.
ISBN-13:	9783319095899
ISBN-10:	3319095897
Sprache:	Englisch
Herstellernummer:	86359370
Einband:	Kartoniert / Broschiert
Autor:	Brémaud, Pierre
Hersteller:	Springer Springer International Publishing AG Universitext
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 22 mm
Von/Mit:	Pierre Brémaud
Erscheinungsdatum:	29.10.2014
Gewicht:	0,604 kg