Related papers: Another look at Second order condition in Extreme …
To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct such examples. It is based on the regularity theory for…
We discuss the problem where the extremal function in embedding theorem of some (generally speaking, non-integer) order is the constant function. We obtain the necessary and sufficient conditions of this.
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
Despite recent successes in Reinforcement Learning, value-based methods often suffer from high variance hindering performance. In this paper, we illustrate this in a continuous control setting where state of the art methods perform poorly…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…
It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various…
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several `items' are given to each participant.…
We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…