Related papers: Extreme Value Distributions for some classes of No…

For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to…

We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is…

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 perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills' inequalities and Mills' ratio for the extended skew-normal distribution and establish the asymptotic…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

Consider an ergodic measure preserving dynamical system $(T,X,\mu)$, and an observable $\phi:X\to\mathbb{R}$. For the time series $X_n(x)=\phi(T^{n}(x))$, we establish limit laws for the maximum process $M_n=\max_{k\leq n}X_k$ in the case…

It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has…

In this paper we study extreme value distributions for one-parameter actions on homogeneous spaces of Lie groups. We study both shortest vectors in unimodular lattices, maximal distance excursions and closest distance returns of a…

For flows whose return map on a cross section has sufficient mixing property, we show that the hitting time distribution of the flow to balls is exponential in limit. We also establish a link between the extreme value distribution of the…

We establish some statistical properties of the hyperbolic times for a class of nonuniformly expanding dynamical systems. The maps arise as factors of area preserving maps of the unit square via a geometric Baker's map type construction,…

Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…

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…

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…

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…

We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily…