Related papers: A Note on Maximum and Minimum Stability of Certain…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
A random variable X is strictly stable if a sum of independent copies of X has the same distribution as X up to scaling, and is stable (in the broad sense) if the sum has the same distribution as X up to both scaling and shifting. Steutel…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
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…
Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly…
We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the…
We obtain the best possible upper bounds for the moments of a single order statistic from independent, non-negative random variables, in terms of the population mean. The main result covers the independent identically distributed case.…
We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual 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},…
We consider Poisson hail models and characterize up to boundaries the collection of critical moments which guarantee stability. In particular, we treat the case of infinite speed of propagation.
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
A generalization of stable and casual stable probability distribution is proposed. The notion of $\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\mathbb Z$ of integers. In contrary…
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…