Fractional fields and applications / Serge Cohen, Jacques Istas

Auteur: Cohen, Serge (1964-) - AuteurCo-auteur: Istas, Jacques (1966-) - AuteurType de document: MonographieCollection: Mathématiques et applications ; 73Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2013Description: 1 vol. (XII-270 p.) : fig. ; 24 cm ISBN: 9783642367380 ; br. Note: This monograph considers fractional Brownian fields and their extensions. Starting with an introductory chapter on stochastic fields and fractal analysis the text continues with a concise discussion of self-similarity with particular emphasis on Gaussian self similar fields. Other topic are Lévy fields and their most important properties. The last two parts of the book deal with more practical issues from statistics and simulation of fractional fields. The text is well written and should be accessible for readers with basic knowledge in probability and stochastic processes. With its wide range of different topics it closes a gap in the existing literature and will be of great use for anybody interested in the topic. (zbMath)Bibliographie: Bibliogr. p. 263-268. Index. Sujets MSC: 60G18 Probability theory and stochastic processes -- Stochastic processes -- Self-similar processes
60G22 Probability theory and stochastic processes -- Stochastic processes -- Fractional processes, including fractional Brownian motion
60-02 Probability theory and stochastic processes -- Research exposition (monographs, survey articles)
60G60 Probability theory and stochastic processes -- Stochastic processes -- Random fields
62M40 Statistics -- Inference from stochastic processes -- Random fields; image analysis
En-ligne: MathSciNet | zbMath | Springerlink

This monograph considers fractional Brownian fields and their extensions. Starting with an introductory chapter on stochastic fields and fractal analysis the text continues with a concise discussion of self-similarity with particular emphasis on Gaussian self similar fields. Other topic are Lévy fields and their most important properties. The last two parts of the book deal with more practical issues from statistics and simulation of fractional fields.

The text is well written and should be accessible for readers with basic knowledge in probability and stochastic processes. With its wide range of different topics it closes a gap in the existing literature and will be of great use for anybody interested in the topic. (zbMath)

Bibliogr. p. 263-268. Index

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