Synopses & Reviews
This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.
Includes bibliographical references (p. 357-393) and index.
Table of Contents
1. Second-Order Analysis of Random Fields. 2. Limit Theorems for Non-Linear Transformations of Random Fields. 3. Asymptotic Distributions of Geometric Functionals of Random Fields. 4. Limit Theorems for Solutions of the Burgers' Equation with Random Data. 5. Statistical Problems for Random Fields with Singular Spectrum. Comments. Bibliography. Index.