Functional Gaussian Approximation for Dependent Structures (Hardcover)

Hardcover. 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 normalapproximations 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 functionalmoderate 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 ofassociation 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. Inaddition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed. This book has its origin in the need of developing and analysing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behaviour of stochastic processes. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. …