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## Weak Convergence of Distributions

*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:
- 10.1093/0198774036.003.0022
- Subject:
- Economics and Finance, Econometrics

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved, and the chapter then considers the ... More

## Weak Convergence in Metric Spaces

*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:
- 10.1093/0198774036.003.0026
- Subject:
- Economics and Finance, Econometrics

This chapter lays the foundations for functional limit theory by considering the case of general metric spaces, from a topological standpoint. It develops tools to replace the method of ... More

## Cadlag Functions

*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:
- 10.1093/0198774036.003.0028
- Subject:
- Economics and Finance, Econometrics

This chapter considers the space D, of functions on the unit interval that are continuous on the right with left limits. D contains and extends the space C, but is nonseparable, so to work with it ... More

## Graph-Theoretic and Linear Algebra Formulations

*Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Steéphane Vialette*

### in Combinatorics of Genome Rearrangements

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262062824
- eISBN:
- 9780262258753
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0006
- Subject:
- Mathematics, Mathematical Biology

This chapter demonstrates the expansion of genome rearrangement problems to a wide mathematical field, including long-standing problems in algebra. It discusses simple permutations and the ... More

## Open Problems

*Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Steéphane Vialette*

### in Combinatorics of Genome Rearrangements

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262062824
- eISBN:
- 9780262258753
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262062824.003.0016
- Subject:
- Mathematics, Mathematical Biology

The variety of genome rearrangement problems is huge and is increasing every year. While it is possible to design many other variants that have yet to be studied, among the most studied variants, ... 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

## Examples and Counterexamples

*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/9780198826941.003.0017
- Subject:
- Mathematics, Probability / Statistics

In this chapter we further comment on the sharpness of several results presented in this monograph, by presenting examples and counterexamples. We study first the moment properties of the renewal ... 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

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