Extreme Value Theory for Dynamical Systems, with Applications in Climate and Neuroscience
Title | Extreme Value Theory for Dynamical Systems, with Applications in Climate and Neuroscience PDF eBook |
Author | Théophile Caby |
Publisher | |
Pages | 0 |
Release | 2019 |
Genre | |
ISBN |
Throughout the thesis, we will discuss, improve and provide a conceptual framework in which methods based on recurrence properties of chaotic dynamics can be understood. We will also provide new EVT-based methods to compute quantities of interest and introduce new useful indicators associated to the dynamics. Our results will have full mathematical rigor, although emphasis will be placed on physical applications and numerical computations, as the use of such methods is developing rapidly. We will start by an introductory chapter to the dynamical theory of extreme events, in which we will describe the principal results of the theory that will be used throughout the thesis. After a small chapter where we introduce some abjects that are characteristic of the invariant measure of the system, namely local dimensions and generalized dimensions, w1 devote the following chapters to the use of EVT to compute such dimensional quantities. One of these method defines naturally a navel global indicator on the hyperbolic properties of the system. ln these chapters, we will present several numerical applications of the methods, bath in real world and idealized systems, and study the influence of different kinds of noise on these indicators. We will then investigate a matter of physical importanc related to EVT: the statistics of visits in some particular small target subsets of the phase-space, in particular for partly random, noisy systems. The results presented in this section are mostly numerical and conjectural, but reveal some universal behavior of the statistics of visits. The eighth chapter makes the connection betweer several local quantities associated to the dynamics and computed using a finite amount of data (local dimensions, hitting times, return times) and the generalized dimensions of the system, that are computable by EVT methods. These relations, stated in the language of large deviation theory (that we will briefly present), have profound physical implications, and constitute a conceptual framework in which the distribution of such computed local quantities can be understood. We then take advantage of these connections to design further methods to compute the generalized dimensions of a system. Finally, in the last part of the thesis, which is more experimental, we extend the dynamical theory of extreme events to more complex observables, which will allow us to study phenomena evolving over long temporal scales. We will consider the example of firing cascades in a model of neural network. Through this example, we will introduce a navel approach to study such complex systems.
Pioneering Works on Extreme Value Theory
Title | Pioneering Works on Extreme Value Theory PDF eBook |
Author | Nobuaki Hoshino |
Publisher | Springer Nature |
Pages | 141 |
Release | 2021-06-04 |
Genre | Mathematics |
ISBN | 9811607680 |
This book presents the state of the art in extreme value theory, with a collection of articles related to a seminal paper on the bivariate extreme value distribution written by Professor Masaaki Sibuya in 1960, demonstrating various developments of the original idea over the last half-century. Written by active researchers, the unique combination of articles allows readers to gain a sense of the excellence of the field, ranging from theory to practice, and the tradition of theoretical developments motivated by practically important issues such as tsunamis and financial crises. The contributions discuss a range of topics, including the parameter estimation of the generalized beta distribution, resampling with the empirical beta copula, and regression analysis on imbalanced binary data, as well as the semiparametric estimation of the upper bound of extrema, the long-term analysis of extreme precipitation over Japanese river basins, and various rules of thumb in hydrology.
Extremes in a Changing Climate
Title | Extremes in a Changing Climate PDF eBook |
Author | Amir AghaKouchak |
Publisher | Springer Science & Business Media |
Pages | 430 |
Release | 2012-10-24 |
Genre | Science |
ISBN | 9400744781 |
This book provides a collection of the state-of-the-art methodologies and approaches suggested for detecting extremes, trend analysis, accounting for nonstationarities, and uncertainties associated with extreme value analysis in a changing climate. This volume is designed so that it can be used as the primary reference on the available methodologies for analysis of climate extremes. Furthermore, the book addresses current hydrometeorologic global data sets and their applications for global scale analysis of extremes. While the main objective is to deliver recent theoretical concepts, several case studies on extreme climate conditions are provided. Audience The book is suitable for teaching in graduate courses in the disciplines of Civil and Environmental Engineering, Earth System Science, Meteorology and Atmospheric Sciences.
Extreme Value Theory and Applications
Title | Extreme Value Theory and Applications PDF eBook |
Author | Janos Galambos |
Publisher | |
Pages | 257 |
Release | 1994-12-01 |
Genre | |
ISBN | 9780788113963 |
Extreme value theory are well defined rules of science that governs disasters, accidents, earthquakes and other unexpected phenomena. It has penetrated the social sciences, the medical profession, economics and even astronomy. The proceedings of this international conference gives equal weight to theory and practice, and was organized to utilize and stimulate progress in the theory of extremes and promote its application. 28 papers presented. Tables and figures.
Extreme Value Theory and Applications
Title | Extreme Value Theory and Applications PDF eBook |
Author | |
Publisher | |
Pages | 280 |
Release | 1994 |
Genre | |
ISBN |
Special Issue on Extreme Value Theory and Applications
Title | Special Issue on Extreme Value Theory and Applications PDF eBook |
Author | |
Publisher | |
Pages | 312 |
Release | 1995 |
Genre | |
ISBN |
Extremes and Recurrence in Dynamical Systems
Title | Extremes and Recurrence in Dynamical Systems PDF eBook |
Author | Lucarini, Valerio Lucarini |
Publisher | |
Pages | 356 |
Release | 2016 |
Genre | Chaotic behavior in systems |
ISBN | 9781118632321 |