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Functional Gaussian Approximation for Dependent Structures$
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Florence Merlev├Ęde, 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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Weakly Associated Random Variables

Weakly Associated Random Variables

­ŁĽâ2-Bounds and Approximation by Independent Structures

(p.233) 7 Weakly Associated Random Variables
Functional Gaussian Approximation for Dependent Structures

Florence Merlev├Ęde

Magda Peligrad

Sergey Utev

Oxford University Press

The purposes of this chapter are to introduce the notion of weakly associated (negatively or positively) random variables and to develop tools that will allow us, in the chapters to follow, to give estimations of moments of partial sums, maximal inequalities, and asymptotic results with both Gaussian and non-gaussian limits. As we shall see, these results shed light on the asymptotic behavior of numerous examples such as exchangeable variables, certain Gaussian processes, empirical processes, various classes of Markov chains, and determinantal processes. They are also useful to study stochastic processes that are functionals of the two independent processes mentioned above.

Keywords:   weak association, weakly negative dependence, weakly positive dependence, approximation inequalities

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