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Mathematiques Et Applications #73: Fractional Fields and Applications

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Mathematiques Et Applications #73: Fractional Fields and Applications Cover

 

Synopses & Reviews

Publisher Comments:

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

Table of Contents

Foreword.- Contents.- Introduction.- Preliminaries.- Self-similarity.- Asymptotic self-similarity.- Statistics.- Simulations.- A Appendix.- B Appendix.- References.

Product Details

ISBN:
9783642367380
Author:
Cohen, Serge
Publisher:
Springer
Author:
Istas, Jacques
Location:
Berlin, Heidelberg
Subject:
Statistics
Subject:
Lévy fields
Subject:
fractional Brownian fields
Subject:
self similarity
Subject:
Simulation
Subject:
Probability Theory and Stochastic Processes
Subject:
Statistical Theory and Methods
Subject:
Engineering design
Subject:
Complexity
Subject:
Statistical Physics, Dynamical Systems and Complexity
Subject:
Science Reference-Technology
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Mathematical statistics
Subject:
Engineering
Copyright:
Edition Description:
2013
Series:
Mathématiques et Applications
Series Volume:
73
Publication Date:
20130502
Binding:
TRADE PAPER
Language:
English
Pages:
290
Dimensions:
235 x 155 mm

Related Subjects


Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Physics
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Physics » General

Mathematiques Et Applications #73: Fractional Fields and Applications New Trade Paper
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Product details 290 pages Springer - English 9783642367380 Reviews:
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