Fourier Analysis and Stochastic Processes / Universitext (PDF)
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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.
- Autor: Pierre Brémaud
- 2014, 2014, 385 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319095900
- ISBN-13: 9783319095905
- Erscheinungsdatum: 16.09.2014
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- Dateiformat: PDF
- Grösse: 4.37 MB
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“This is clearly an academic text, very well written and organized, with a high pedagogical quality … . This is a very interesting book adequate to support Master or PhD courses in Stochastic Processes. … it is accessible to larger audiences and useful for professionals working, for instance, in electrical engineering and communications, biology, economics and finance, but not only.” (Manuel Alberto M. Ferreira, Journal of Mathematics and Technology, Vol. 6 (1), 2015)
“This is a nice and modern book on the Fourier theory of functions, finite measures and stochastic processes with a lot of examples and exercises. … it may also be accessible to a large audience (electrical engineers, biologists and economists), since the author made the text as self contained as possible and provided a lot of examples in each chapter relevant from the point of view of applications. I warmly recommend the book for graduate students and researchers as well.” (Mátyás Barczy, Acta Scientiarum Mathematicarum, Vol. 81 (3-4), 2015)
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