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Tuesday, July 28, 2020 | History

1 edition of Limit Theorems for Random Fields with Singular Spectrum found in the catalog.

Limit Theorems for Random Fields with Singular Spectrum

by Nikolai Leonenko

  • 216 Want to read
  • 9 Currently reading

Published by Springer Netherlands, Imprint, Springer in Dordrecht .
Written in English


About the Edition

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.

Edition Notes

Statementby Nikolai Leonenko
SeriesMathematics and Its Applications -- 465, Mathematics and Its Applications -- 465.
The Physical Object
Format[electronic resource] /
Pagination1 online resource (416 pages).
Number of Pages416
ID Numbers
Open LibraryOL27071227M
ISBN 109401146071
ISBN 109789401146074
OCLC/WorldCa840310845

Random Bag. Random Bag Nuts Bolts From Dismantle Yamaha Fz8 Fz 8 Fz8n $ Applied Mathematics Department at Brown University. Courses. UNDERGRADUATE COURSES. APMA Introduction to Modeling Topics of Applied Mathematics, introduced in the context of practical applications where defining the problems and understanding what kinds of solutions they can have is the central issue.

ary processes with singular spectra. 1. Introduction. During the last thirty years, a number of papers have been devoted to limit theorems for nonlinear transformations of Gaussian processes and random fields. The pioneering results are those of Taqqu [25, 26] and Dobrushin and Major [6], for convergence to Gaussian and non-Gaussian. (source: Nielsen Book Data) Random and ergodic Schrodinger operators, singular continuous spectrum: A new approach to spectral gap problems by J. Bourgain Strictly ergodic subshifts and associated operators by D. Damanik Lyapunov exponents and spectral analysis of ergodic Schrodinger operators: A survey of Kotani theory and its applications by.

  This paper discusses the asymptotic distributions of a class of M-estimators in non-linear regression models with long-range dependence (LRD). Such models arise in applications in hydrology, economics and other sciences(see, for example, Beran()) Statistical problems for discrete parameter processes with LRD were studied by many authors. Beran's () book contains a pretty complete. I have recently uploaded the paper arXiv [] entitled Spectrum of non-Hermitian heavy tailed random matrices, written in collaboration with Charles Bordenave and Pietro Caputo. We provide a rigorous analysis of the phenomenon behind the pictures above. Let \({(X_{jk})_{j,k\geq1}} \) be i.i.d. complex random variables with cumulative distribution function \({F} \).


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Leonenko,available at Book Depository with free delivery worldwide. Second-Order Analysis of Random Fields Limit Theorems for Non-Linear Transformations of Random Fields Asymptotic Distributions of Geometric Functionals of Random Fields Limit Theorems for Solutions of the Burgers' Equation with Random Data Statistical Problems for Random Fields with Singular Spectrum.

Series Title. 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.

Limit Theorems for Random Fields with Singular Spectrum. Authors (view affiliations) Nikolai Leonenko Limit Theorems for Non-Linear Transformations of Random Fields. Nikolai Leonenko. Pages Asymptotic Distributions of Geometric Functionals of Random Fields.

Nikolai Leonenko. Pages Limit Theorems for Solutions of the. Free 2-day shipping. Buy Mathematics and Its Applications: Limit Theorems for Random Fields with Singular Spectrum (Paperback) at a limit theorem for random fields with a singularity in the spectrum W e consider the random fields whose sp ectra Φ (λ) hav e singularities at a p oint λ = a =0, that is, o n the sphere.

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and. Leonenko N. () Statistical Problems for Random Fields with Singular Spectrum.

In: Limit Theorems for Random Fields with Singular Spectrum. Mathematics and Its Applications, vol Author: Nikolai Leonenko. 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. Theory of Probability & Its Applications() An example of stability of singular spectrum under smooth perturbations.

Integral Equations and Operator Theory() Limit theorems for random number of random elements on complete separable metric by: [] Leonenko, N. () Limit Theorems for Random Fields with Singular Spectrum, Kluwer.

[] Leonenko, N., Sakhno, L. () On spectral representations of tensor random fields on Author: Domenico Marinucci, Giovanni Peccati. () Some limit theorems for independent random processes at random points in time and random elements defined by them. Journal of Mathematical Sciences() Simulation of random processes and rate-distortion by: The problem of regression models for homogeneous and isotropic random fields observed on a sphere of increasing radius was considered by Yadrenko, Ivanov and Leonenko and others.

We consider spherical regression model with LRD random noise (or with singular Cited by: 1. Nikolai Leonenko, Limit theorems for random fields with singular spectrum, Mathematics and its Applications, vol.

Kluwer Academic Publishers, Dordrecht, MR 8. Contents: We state limit theorems for the integrals, in Sections 2 Main results and discussion, 5 Non-homogeneous random fields respectively, with discussion of the assumptions used and of some possible applications. The example of Gaussian fields is discussed in Section 3, and an invariance principle provided in Section by: 3.

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“Limit theorems for sums of random exponentials”, Probab. theory related fields,v(with G. Ben Arous, L. Bogachev) Transition from the annealed to the quenched asymptotics for a random walk on random obstacles, Annals of Probability, 33 (), #6, pp (with G.

Ben Arous, A. Ramirez). Spectral theory of random fields. We study the basic spectral representations of different classes of random fields, which play the main role in probabilistic and statistical analysis of random fields. One of the first book devoted to spectral analysis of random fields.

This book offers a superb overview of limit theorems and probability inequalities for sums of independent random variables. Unique in its combination of both classic and recent results, the book details the many practical aspects of these important tools for solving a great variety of .Limit theorems for large deviations L.

Saulis, V.A. Statulevicius Revised, updated, and translated from the Russian edition, describes the application of the method of cumulants to limit theorems on large deviations, in such a manner as to be of interest to researchers and graduate students working on probability theory, mathematical.

Abstract. Two critical properties of stationary random fields are their degree of smoothness and the rate of decay of correlation at long lags. These properties are in turn closely connected to the behaviour of the random fields’ spectral densities at infinity and at the origin, by: 9.