Extremes and recurrence in dynamical systems / Valerio Lucarini [and eight others].

Format:

Book

Author/Creator:

Lucarini, V. (Valerio), author.

Series:

Pure and applied mathematics (John Wiley & Sons : Unnumbered)

Pure and applied mathematics : a Wiley series of texts, monographs, and tracts

Language:

English

Subjects (All):

Chaotic behavior in systems.

Stochastic processes.

Probabilities.

Extreme value theory.

Dynamics.

Physical Description:

1 online resource (356 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : John Wiley & Sons, Incorporated, [2016]

Language Note:

English

Summary:

Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: * A careful examination of how a dynamical system can serve as a generator of stochastic processes * Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes * Several examples of analysis of extremes in a physical and geophysical context * A final summary of the main results presented along with a guide to future research projects * An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l'environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.

Contents:

Title Page; COPYRIGHT; Table of Contents; DEDICATION; CHAPTER 1: INTRODUCTION; 1.1 A TRANSDISCIPLINARY RESEARCH AREA; 1.2 SOME MATHEMATICAL IDEAS; 1.3 SOME DIFFICULTIES AND CHALLENGES IN STUDYING EXTREMES; 1.4 EXTREMES, OBSERVABLES, AND DYNAMICS; 1.5 THIS BOOK; ACKNOWLEDGMENTS; CHAPTER 2: A FRAMEWORK FOR RARE EVENTS IN STOCHASTIC PROCESSES AND DYNAMICAL SYSTEMS; 2.1 Introducing Rare Events; 2.2 Extremal Order Statistics; 2.3 Extremes and Dynamics; CHAPTER 3: CLASSICAL EXTREME VALUE THEORY; 3.1 THE i.i.d. SETTING AND THE CLASSICAL RESULTS; 3.2 STATIONARY SEQUENCES AND DEPENDENCE CONDITIONS

3.3 CONVERGENCE OF POINT PROCESSES OF RARE EVENTS3.4 ELEMENTS OF DECLUSTERING; CHAPTER 4: EMERGENCE OF EXTREME VALUE LAWS FOR DYNAMICAL SYSTEMS; 4.1 EXTREMES FOR GENERAL STATIONARY PROCESSES-AN UPGRADE MOTIVATED BY DYNAMICS; 4.2 EXTREME VALUES FOR DYNAMICALLY DEFINED STOCHASTIC PROCESSES; 4.3 POINT PROCESSES OF RARE EVENTS; 4.4 CONDITIONS Дq(un), D3(un), Dp(un)* AND DECAY OF CORRELATIONS; 4.5 SPECIFIC DYNAMICAL SYSTEMS WHERE THE DICHOTOMY APPLIES; 4.6 EXTREME VALUE LAWS FOR PHYSICAL OBSERVABLES; CHAPTER 5: HITTING AND RETURN TIME STATISTICS

5.1 INTRODUCTION TO HITTING AND RETURN TIME STATISTICS5.2 HTS VERSUS RTS AND POSSIBLE LIMIT LAWS; 5.3 THE LINK BETWEEN HITTING TIMES AND EXTREME VALUES; 5.4 UNIFORMLY HYPERBOLIC SYSTEMS; 5.5 NONUNIFORMLY HYPERBOLIC SYSTEMS; 5.6 NONEXPONENTIAL LAWS; CHAPTER 6: EXTREME VALUE THEORY FOR SELECTED DYNAMICAL SYSTEMS; 6.1 RARE EVENTS AND DYNAMICAL SYSTEMS; 6.2 INTRODUCTION AND BACKGROUND ON EXTREMES IN DYNAMICAL SYSTEMS; 6.3 THE BLOCKING ARGUMENT FOR NONUNIFORMLY EXPANDING SYSTEMS; 6.4 NONUNIFORMLY EXPANDING DYNAMICAL SYSTEMS; 6.5 NONUNIFORMLY HYPERBOLIC SYSTEMS; 6.6 HYPERBOLIC DYNAMICAL SYSTEMS

6.7 SKEW-PRODUCT EXTENSIONS OF DYNAMICAL SYSTEMS6.8 ON THE RATE OF CONVERGENCE TO AN EXTREME VALUE DISTRIBUTION; 6.9 EXTREME VALUE THEORY FOR DETERMINISTIC FLOWS; 6.10 PHYSICAL OBSERVABLES AND EXTREME VALUE THEORY; 6.11 NONUNIFORMLY HYPERBOLIC EXAMPLES: THE HÉNON AND LOZI MAPS; 6.12 Extreme Value Statistics for the Lorenz '63 Model; CHAPTER 7: EXTREME VALUE THEORY FOR RANDOMLY PERTURBED DYNAMICAL SYSTEMS; 7.1 INTRODUCTION; 7.2 Random Transformations via the Probabilistic Approach: Additive Noise; 7.3 Random Transformations via the Spectral Approach

7.4 RANDOM TRANSFORMATIONS VIA THE PROBABILISTIC APPROACH: RANDOMLY APPLIED STOCHASTIC PERTURBATIONS7.5 OBSERVATIONAL NOISE; 7.6 NONSTATIONARITY-THE SEQUENTIAL CASE; CHAPTER 8: A STATISTICAL MECHANICAL POINT OF VIEW; 8.1 CHOOSING A MATHEMATICAL FRAMEWORK; 8.2 GENERALIZED PARETO DISTRIBUTIONS FOR OBSERVABLES OF DYNAMICAL SYSTEMS; 8.3 IMPACTS OF PERTURBATIONS: RESPONSE THEORY FOR EXTREMES; 8.4 REMARKS ON THE GEOMETRY AND THE SYMMETRIES OF THE PROBLEM; CHAPTER 9: Extremes as Dynamical and Geometrical Indicators; 9.1 The Block Maxima Approach; 9.2 The Peaks Over Threshold Approach

9.3 Numerical Experiments: Maps Having Lebesgue Invariant Measure

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-118-63235-4

1-118-63229-X

OCLC:

931226998