UID:
almahu_9947363376302882
Umfang:
VIII, 406 p.
,
online resource.
ISBN:
9789401146074
Serie:
Mathematics and Its Applications ; 465
Anmerkung:
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 with Singular 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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9789401059473
Sprache:
Englisch
DOI:
10.1007/978-94-011-4607-4
URL:
http://dx.doi.org/10.1007/978-94-011-4607-4
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