Related papers: Limits of interval orders and semiorders
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that…
In this paper we present some bounds of Hausdorff measures of objects definable in o-minimal structures: sets, fibers of maps, inverse images of curves of maps, etc. Moreover, we also give some explicit bounds for semi-algebraic or…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
We consider almost upper semi-continuous processes defined on a finite Markov chain. The distributions of the functionals associated with the exit from a finite interval are studied. We also consider some modification of these processes.
In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that the total variation of functions of bounded variation is lower semicontinuous with respect to $L^1$-convergence in…
This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…
This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a…
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 investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible…
This paper is devoted to studying difference indices of quasi-regular difference algebraic systems. We give the definition of difference indices through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved.…
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…
We discuss limit distributions for hitting-time functions of certain exceptional families of asymptotically rare events for ergodic probability preserving transformations. The abstract core is an inducing argument. The latter applies, for…
This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…
In this article, we present a new method to study uniqueness of form extensions in a rather general setting. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. Our main abstract result…
Over time, there have hen refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distributions depict a complete ordering among the propositions of interest, yet…