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Monday, July 27, 2020 | History

9 edition of Limit theorems for associated random fields and related systems found in the catalog.

Limit theorems for associated random fields and related systems

A. V. BulinskiД­

Limit theorems for associated random fields and related systems

by A. V. BulinskiД­

  • 16 Want to read
  • 3 Currently reading

Published by World Scientific in New Jersey .
Written in English

    Subjects:
  • Random fields,
  • Limit theorems (Probability theory)

  • Edition Notes

    Includes bibliographical references (p. 411-430) and indexes

    StatementAlexander Bulinski & Alexey Shashkin
    SeriesAdvanced series on statistical science and applied probability -- v. 10
    ContributionsShashkin, Alexey
    Classifications
    LC ClassificationsQA274.45 .B85 2007
    The Physical Object
    Paginationx, 436 p. ;
    Number of Pages436
    ID Numbers
    Open LibraryOL17256612M
    ISBN 109812709401
    ISBN 109789812709400
    LC Control Number2007023102

    The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on ℝ d are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for additive functionals of such systems is established.

      A functional central limit theorem for the level measure of a Gaussian random field. Author links open overlay panel A. Shashkin. Show more. A. Bulinski, A. ShashkinLimit theorems for associated random fields and related systems. Limit theorems for random fields. [Nguyen Van Thu] Book: All Authors / Contributors: Nguyen Van Thu. Find more information about: ISBN: X Related Subjects: (4) Random fields. Limit theorems (Probability theory) Grenzwertsatz. Zufälliges Feld.

    LIMIT THEOREMS FOR RANDOM WALKS 5 by p, a probability density on Zd. Then L= I−R, where Iis the identity operator, can be considered as minus the Markov generator of the associated random walk. For a proper function ψwe may define a subordinate random walk Sψas the random walk process with the generator−ψ(L). The Central Limit Theorem (for the mean) If random variable X is defined as the average of n independent and identically distributed random variables, X 1, X 2, , X n; with mean, µ,and Sd, σ. Then, for large enough n (typically n≥30), X n is approximately Normally distributed with parameters: µ x = µ and σ x = σ/ n.


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Limit theorems for associated random fields and related systems by A. V. BulinskiД­ Download PDF EPUB FB2

July 5, World Scienti c Book - in x in ws-book n_new viii Limit Theorems for Associated Random Fields and Related Systems in that research domain. Get this from a library. Limit theorems for associated random fields and related systems.

[A V Bulinskiĭ; A P Shashkin]. Limit theorems for associated random fields and related systems. New Jersey: World Scientific, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: A V Bulinskiĭ; A P Shashkin.

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They have found many applications in limit theorems for random fields [26, ]. Even if the extension of PA to point processes have been used in analysis of functionals of random measures [29, Then, moment inequalities for sums of dependent random variables are stated which yield e.g.

the asymptotic behaviour of the variance of these sums which is essential for the proof of limit theorems. Finally, central limit theorems for dependent random fields are given.

Abstract. We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi- positively or negatively) associated random fields with stochastically continuous realizations for a fixed excursion level.

Abstract. A new variant of the CLT is established for random fields defined on ℝ d which are strictly stationary, with a finite second moment and weakly dependent (comprising cases of positive or negative association). The summation domains grow in the van Hove sense.

At the same time the indices of observations form more and more dense grids in these domains. 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. Stationary quasi-associated random fields with continuous covariance function are considered.

Recently, Bulinski, Spodarev, and Timmermann proved a central limit theorem for the excursion set volumes of such random fields. We establish a functional version of this theorem.

Bibliography: 11 titles. Abstract. This chapter gives preliminaries on random fields necessary for understanding of the next two chapters on limit theorems.

Basic classes of random fields (Gaussian, stable, infinitely divisible, Markov and Gibbs fields, etc.) are considered. Limit Theorems for Random Fields with Singular Spectrum by N.

Leonenko,available at Book Depository with free delivery worldwide. () A central limit theorem for functions of stationary max-stable random fields on R d.

Stochastic Processes and their Applications() Methods for estimating the upcrossings index: improvements and comparison. Limit theorems for associated fields and related systems.

and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in. Limit theorems for associated random fields and related systems Central limit theorems for the excursion sets volumes of weakly dependent random fields Jan () A central limit theorem for functions of stationary max-stable random fields on R d.

Stochastic Processes and their Applications() Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments. The limits of the numerator and denominator follow from Theorems 1, 2, and 4. The limit of the fraction follows from Theorem 3.

Limits of polynomials. The student might think that to evaluate a limit as x approaches a value, all we do is evaluate the function at that value. Limit Theorems for Associated Random Fields and Related Systems, Advanced Series on Statistical Science & Applied Probability, vol.

10, World Scientific Publishing Co. Pvt. Ltd., Hackensack, NJ (). This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems.

The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions.

More precisely, we deal with random fields of the form X k = g (ε k − s, s ∈ Z d), k ∈ Z d, where (ε i) i ∈ Z d are iid random variables and g is a measurable function. Probability Theory and Related FieldsLyapunov exponents: A survey. Finite ensemble averages of the zero-temperature resistance and conductance of disordered one-dimensional systems.

Physical Review B A Variant of the Local Limit Theorem for Products of Random Matrices. Theory of Probability & Its. 3. Baum–Katz type theorems for ND random fields. The first two theorems of this Section are extensions and compliments of some results of Peligrad, Gut et al., Kuczmaszewska et al.

Theorem Let r ≥ 1, α 1 > 1 2, α 1 r ≥ 1 and {X n, n ∈ N d} be a zero mean random.Limit Theorems in probability theory, a group of theorems that give the conditions governing the appearance of specific regularities as a result of the action of a large number of random factors.

Historically, the first limit theorems were Bernoulli’s theorem, which was set forth inand the Laplace theorem, which was published in These.