Functional Gaussian Approximation for Dependent Structures

Functional Gaussian Approximation for Dependent Structures
ISBN-10
0192561863
ISBN-13
9780192561862
Category
Mathematics
Pages
496
Language
English
Published
2019-02-14
Publisher
Oxford University Press
Authors
Florence Merlevède, Magda Peligrad, Sergey Utev

Description

Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations 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 and functional moderate deviation principle. The results 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. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are 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 analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Similar books