Limit Theorems for Random Fields with Singular Spectrum
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
1999, 1999
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Edition: | 1st ed. 1999 |
Series: | Mathematics and Its Applications
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Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Second-Order Analysis of Random Fields
- 1.1 Basic Concepts and Notation
- 1.2 Elements of Spectral Theory of Random Fields
- 1.3 Models of Random Processes and Fields with Singular Spectrum
- 1.4 Tauberian and Abelian Theorems for Correlation Function of Homogeneous Isotropic Random Fields
- 2 Limit Theorems for Non-Linear Transformations of Random Fields
- 2.1 Some Properties of Gaussian and X-Squared Random Fields
- 2.2 Reduction Theorems for the Local Functionals of Random Fields with Slowly Decaying Correlations
- 2.3 Multiple Stochastic Integrals
- 2.4 Non-Central Limit Theorems for Local Functionals of Random Fields
- 3 Asymptotic Distributions of Geometric Functionals of Random Fields
- 3.1 Limit Distributions for Characteristics of the Excess above a Level for Gaussian Fields
- 3.2 Limiting Distributions for the Excess Over a Radial Surface of X-Squared Random Fields
- 3.3 Spherical Measures of Excess over of Moving Level
- 3.4 Sojourns of Multi-Dimensional Gaussian Fields with Dependent Components
- 3.5 Asymptotic Normality of Random ‘Area of Surface’ of Planar Gaussian Field
- 3.6 Asymptotics for Occupation Densities of Gaussian and X-Squared Random Fields
- 4 Limit Theorems For Solutions of The Burgers’ Equation with Random Data
- 4.1 Physical Motivation and Recent History
- 4.2 Hopf-Cole Solution
- 4.3 Parabolic Asymptotics for Weakly Dependent Random Data: the Gaussian Scenario
- 4.4 Parabolic Limits for Strongly Dependent Random Initial Conditions: the Gaussian Scenario
- 4.5 Parabolic Limits for Strongly Dependent Random Data: the Non-Gaussian Scenario
- 4.6 Exact Parabolic Asymptotics for Singular Burgers’ Equation
- 4.7 Hyperbolic Asymptotics for Rescaled Solutions of Burgers’ Equation
- 5 Statistical Problems for Random Fields withSingular Spectrum
- 5.1 Estimation of Mathematical Expectation
- 5.2 Estimation of the Covariance Function
- 5.3 Efficient Estimation of Regression Coefficients of a Random Fields Observed on the Sphere
- 5.4 Estimation in the Frequency Domain
- Comments