Related papers: Extreme values and the level-crossing problem. An …
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
In this work, we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu…
Let $K_n$ denote the number of distinct values among the first $n$ terms of an infinite exchangeable sequence of random variables $(X_1,X_2,\ldots)$. We prove for $n=3$ that the extreme points of the convex set of all possible laws of $K_3$…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
We study standard processes with no negative jumps under the entrance boundary condition. Similarly to one-dimensional diffusions, we show that the process can be made into a Feller process by attaching the boundary point to the state…
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We study the extremal processes through Feller semigroups theory from which it is possible to observe some parallelism with subordinators. Consequently, we observe that an extremal process possesses concepts analogous to those of Laplace…
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 explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We obtain limit theorems for the row extrema of a triangular array of zero-modified geometric random variables. Some of this is used to obtain limit theorems for the maximum family size within a generation of a simple branching process with…
This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring…
We continue here the study of free extreme values begun in Ben Arous and Voiculescu (2006). We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure (Voiculescu (1998),…