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Limit Theorems for Random Fields with Singular Spectrum

Bibliographic Details
Main Author: Leonenko, Nicolai
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1999, 1999
Edition:1st ed. 1999
Series:Mathematics and Its Applications
Subjects:
Continuum Mechanics
Statistics 
Probability Theory
Applications Of Mathematics
Statistics
Mathematics
Probabilities
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

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