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## 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

## Application to the Uniform Laws of Large Numbers for Dependent 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/9780198826941.003.0016
- Subject:
- Mathematics, Probability / Statistics

As mentioned in Chapter 5, one of the most powerful techniques to derive limit theorems for partial sums associated with a sequence of random variables which is mixing in some sense is the coupling ... More

## Functional Gaussian Approximation for Dependent Structures

*Florence Merlevède, Magda Peligrad, and Sergey Utev*

- Published in print:
- 2019
- Published Online:
- April 2019
- ISBN:
- 9780198826941
- eISBN:
- 9780191865961
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198826941.001.0001
- Subject:
- Mathematics, Probability / Statistics

This book has its origin in the need for developing and analyzing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure ... 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

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