Functional Gaussian Approximation for Dependent Structures
Florence Merlevède, Magda Peligrad, and Sergey Utev
Abstract
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 and asymptotic behavior of stochastic processes. This monograph has double scope. First, to present tools for dealing with dependent structures directed toward obtaining normal approximations. Second, to apply the normal approximations presented in the book to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including ... More
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 and asymptotic behavior of stochastic processes. This monograph has double scope. First, to present tools for dealing with dependent structures directed toward obtaining normal approximations. Second, to apply the normal approximations presented in the book to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem (CLT) and functional moderate deviation principle (MDP). The results will point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. Over the course of the book different types of dependence structures are considered, ranging from the traditional mixing structures to martingale-like structures and to weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications have been carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analyzing new data in economics, linear processes with dependent innovations will also be considered and analyzed.
Keywords:
central limit theorem,
invariance principles,
maximal moment inequalities,
dependent random variables,
mixing sequences,
martingale-like sequences,
negative dependence
Bibliographic Information
Print publication date: 2019 |
Print ISBN-13: 9780198826941 |
Published to Oxford Scholarship Online: April 2019 |
DOI:10.1093/oso/9780198826941.001.0001 |
Authors
Affiliations are at time of print publication.
Florence Merlevède, author
Professor, Université Paris-Est Marne-La-Vallée
Magda Peligrad, author
Professor, University of Cincinnati
Sergey Utev, author
University of Leicester, Professor
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