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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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