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Functional Gaussian Approximation for Dependent Structures$
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Florence Merlevède, Magda Peligrad, and Sergey Utev

Print publication date: 2019

Print ISBN-13: 9780198826941

Published to Oxford Scholarship Online: April 2019

DOI: 10.1093/oso/9780198826941.001.0001

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Examples of Stationary Sequences with Approximate Negative Dependence

Examples of Stationary Sequences with Approximate Negative Dependence

Chapter:
(p.305) 10 Examples of Stationary Sequences with Approximate Negative Dependence
Source:
Functional Gaussian Approximation for Dependent Structures
Author(s):

Florence Merlevède

Magda Peligrad

Sergey Utev

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198826941.003.0010

In this chapter, we treat several examples of stationary processes which are asymptotically negatively dependent and for which the results of Chapter 9 apply. Many systems in nature are complex, consisting of the contributions of several independent components. Our first examples are functions of two independent sequences, one negatively dependent and one interlaced mixing. For instance, the class of asymptotic negatively dependent random variables is used to treat functions of a determinantal point process and a Gaussian process with a positive continuous spectral density. Another example is point processes based on asymptotically negatively or positively associated sequences and displaced according to a Gaussian sequence with a positive continuous spectral density. Other examples include exchangeable processes, the weighted empirical process, and the exchangeable determinantal point process.

Keywords:   determinantal process, displaced point process, exchangeable processes

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