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Weak Convergence in a Function Space

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0027
Subject:
Economics and Finance, Econometrics

This chapter applies the theory of Ch. 26 to the case of the space C of continuous functions on the unit interval. It is shown how to assign probability measures to C, and Weiner measure (Brownian ... More


Gaussian Approximation via Martingale Methods

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0004
Subject:
Mathematics, Probability / Statistics

Gordin’s seminal paper (1969) initiated a line of research in which limit theorems for stationary sequences are proved via appropriate approximations by stationary martingale difference sequences ... More


Moment Inequalities and Gaussian Approximation for Mixing Sequences

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0006
Subject:
Mathematics, Probability / Statistics

Although the “mixing assumption” is nowadays considered as a rather restrictive condition, it is a powerful tool, which possesses strong properties such as preservation under functional transform, ... More


Reversible Markov Chains

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0014
Subject:
Mathematics, Probability / Statistics

This chapter is dedicated to the Gaussian approximation of a reversible Markov chain. Regarding this problem, the coefficients of dependence for reversible Markov chains are actually the covariances ... More


Moment Inequalities and Gaussian Approximation for Martingales

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0002
Subject:
Mathematics, Probability / Statistics

The aim of this chapter is to present useful tools for analyzing the asymptotic behavior of partial sums associated with dependent sequences, by approximating them with martingales. We start by ... More


Gaussian Approximation under Asymptotic Negative Dependence

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0009
Subject:
Mathematics, Probability / Statistics

Here we introduce the notion of asymptotic weakly associated dependence conditions, the practical applications of which will be discussed in the next chapter. The theoretical importance of this class ... More


Functional Central Limit Theorem for Empirical Processes

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0015
Subject:
Mathematics, Probability / Statistics

Here we discuss the Gaussian approximation for the empirical process under different kinds of dependence assumptions for the underlying stationary sequence. First, we state a general criterion to ... More


Random Walk in Random Scenery

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0013
Subject:
Mathematics, Probability / Statistics

In this chapter we investigate the question of central limit behavior and its functional form for the partial sums associated with a centered L2-stationary sequence of real-valued random variables ... More


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