Related papers: Generalized Extreme Value distribution parameters …
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals…
Extreme Value Theory (EVT) is exploited to determine the global stability threshold $R_g$ of plane Couette flow --the flow of a viscous fluid in the space between two parallel plates-- whose laminar or turbulent behavior depends on the…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process:…
Automatic differentiation provides an efficient means of computing derivatives of complex functions with machine precision, thereby enabling differentiable simulation. In this work, we propose the use of the norm of the tangent map,…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a…
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
We give a brief account of application of extreme value theory in dynamical systems by using perturbation techniques associated to the transfer operator. We will apply it to the baker's map and we will get a precise formula for the extremal…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of…
As part of global climate change an accelerated hydrologic cycle (including an increase in heavy precipitation) is anticipated. So, it is of great importance to be able to quantify high-impact hydrologic relationships, for example, the…
I propose a new procedure to estimate the False Alarm Probability, the measure of significance for peaks of periodograms. The key element of the new procedure is the use of generalized extreme-value distributions, the limiting distribution…
In this paper, we analyze several instrumental records of temperatures at different locations by using new techniques originally developed for the analysis of extreme values of dynamical systems. We show that they have the same recurrence…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…