Limit Theorems for Random Fields with Singular Spectrum (Hardcover, 1999 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 465
Release date:	2001
First published:	1999
Authors:	Nicolai Leonenko
Dimensions:	235 x 155 x 23mm (L x W x T)
Format:	Hardcover
Pages:	406
Edition:	1999 ed.
ISBN-13:	978-0-7923-5635-6
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics Promotions
LSN:	0-7923-5635-7
Barcode:	9780792356356

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