Fourier Analysis and Stochastic Processes

2014
ISBN: 978-3-319-09589-9
Verlag: Springer International Publishing

Buch, Englisch, 385 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 6029 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Brémaud, Pierre

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

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.

Über Autor(innen)

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