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portada Limit Theorems for Random Fields with Singular Spectrum
Type
Physical Book
Author
Publisher
Language
English
Pages
406
Format
Paperback
Dimensions
23.4 x 15.6 x 2.2 cm
Weight
0.59 kg.
ISBN13
9789401059473
Categories

Limit Theorems for Random Fields with Singular Spectrum

Nicolai Leonenko (Author) · Springer · Paperback

Limit Theorems for Random Fields with Singular Spectrum - Leonenko, Nicolai

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Synopsis "Limit Theorems for Random Fields with Singular Spectrum"

This book is devoted to an investigation of the basic problems of the the- ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran- dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ significantly from the theory of weakly dependent random fields. The first chapter presents basic concepts of the spectral theory of random fields, some examples of random processes and fields with singular spectrum, Tauberian and Abelian theorems for the covariance function of singular ran- dom fields. In the second chapter limit theorems for non-linear functionals of random fields with singular spectrum are proved. Chapter 3 summarizes some limit theorems for geometric functionals of random fields with long-range dependence. Limit distributions of the solutions of Burgers equation with random data via parabolic and hyperbolic rescaling are presented in chapter 4. And chapter 5 presents some problems of statistical analysis of random fields with singular spectrum. I would like to thank the editor, Michiel Hazewinkel, for his support. I am grateful to the following students and colleagues: 1. Deriev, A. Olenko, K. Rybasov, L. Sakhno, M. Sharapov, A. Sikorskii, M. Silac-BenSic. I would also like to thank V.Anh, O. Barndorff-Nielsen, Yu. Belyaev, P.

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