Fourier Analysis and Stochastic Processes

  • Pierre Brémaud

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pierre Brémaud
    Pages 1-90
  3. Pierre Brémaud
    Pages 91-118
  4. Pierre Brémaud
    Pages 119-179
  5. Pierre Brémaud
    Pages 181-258
  6. Pierre Brémaud
    Pages 259-336
  7. Back Matter
    Pages 337-385

About this book


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).

A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spaces in the first chapter) make the book self-contained. 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.


Point Processes Power Spectral Measure Second-Order Stochastic Processes Stochastic Processes Time Series

Authors and affiliations

  • Pierre Brémaud
    • 1
  1. 1.InriaParisFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-09589-9
  • Online ISBN 978-3-319-09590-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book