Bøger af Paul Doukhan

Time series research has been an area of considerable research activity over the past several decades. The essential ingredient --- the notion of time-dependence --- is required for measuring and then accurately predicting data to construct suitable models for diverse phenomena. This fairly self-contained volume, written by leading experts in their respective fields, especially focuses on the theoretical concepts, methodologies, and practical applications pertaining to self-similar processes and long-range dependent phenomena. Graduate students, researchers, and professionals in industry will benefit from the book.

Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. The second part describes mixing properties of classical processes and random fields as well as providing a detailed study of linear and Gaussian fields.

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory.