Related papers: Extreme Value Laws for sequences of intermittent m…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
The maxima and the minima of a randomly stopped sample of a random variable, $X$, together with two newly defined random variables that make $X$ into the maxima or minima of a randomly stopped sample of them, can be used to define…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the…
Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…
We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…