Stable non-Gaussian self-similar processes with stationary increments [electronic resource] /
Pipiras, Vladas.author.
Taqqu, Murad S.author.
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
Includes bibliographical references and index.
Preliminaries -- Minimality, Rigidity, and Flows -- Mixed Moving Averages and Self-similarity -- A. Historical Notes -- B. Standard Lebesgue Spaces and Projections -- C. Notation Summary.
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
Probabilities.
Dynamics.
Ergodic theory.
Probability Theory and Stochastic Processes.
Dynamical Systems and Ergodic Theory.