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Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
In this work, we propose a simulation-based estimation approach using generative neural networks to determine dependencies of precipitation maxima and their underlying uncertainty in time and space. Within the common framework of max-stable…
This paper presents an initial exploration of high frequency records of extreme wind speed in two steps. The first consists in finding the suitable extreme distribution for $120$ measuring stations in Switzerland, by comparing three known…
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…
Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…
Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…
For centuries, soaring birds -- such as albatrosses and eagles -- have been mysterious and intriguing for biologists, physicists, aeronautical/control engineers, and applied mathematicians. These fascinating biological organisms have the…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
Climate change poses an extreme threat to biodiversity, making it imperative to efficiently model the geographical range of different species. The availability of large-scale remote sensing images and environmental data has facilitated the…
The spread of invasive species can have far reaching environmental and ecological consequences. Understanding invasion spread patterns and the underlying process driving invasions are key to predicting and managing invasions. We combine a…
Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-$t$ process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with…
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…
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…
In this paper we prove the existence of Extreme Value Laws for dynamical systems perturbed by instrument-like-error, also called observational noise. An orbit perturbed with observational noise mimics the behavior of an instrumentally…
Quantifying animal interactions is crucial for understanding various ecological processes, including social community structures, predator-prey dynamics, spreading of pathogens and information. Despite the ubiquity of interaction processes…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…