Convergence of copulas: critical remarks

We study some aspects of the relationship between the weak convergence of sequences of multivariate distribution functions and the pointwise convergence of the copulas that connect them to their respective marginals

Semicopulae

We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, t-nor

Probabilistic norms and convergence of random variables

We prove that probabilistic norms of suitable Probabilistic Normed spaces induce convergence in probability,L^p convergence and almost sure convergence

La convergenza debole di F. R. a r dimensioni

Abstract

A primer on triangle functions II

In [32] we presented an overview of concepts, facts and results on triangle functions based on the notions of t-norm, copula, (generalized) convolution, semicopula, quasi-copula. Here, we continue our presentation. In particular, we treat the concept of duality and study a few important cases of functional equations and inequalities for triangle functions like, e.g., convolution, Cauchy's equation, dominance, and Jensen convexity

A study of boundedness in probabilistic normed spaces

It was shown in Lafuerza-Guillén, Rodríguez- Lallena and Sempi (1999) that uniform boundedness in a Serstnev PN space (V,\un, \tau,\tau^*), (named boundeness in the present setting) of a subset A in V with respect to the strong topology is equivalent to the fact that the probabilistic radius R_A of A is an element of D^+. Here we extend the equivalence just mentioned to a larger class of PN spaces, namely those PN spaces that are topological vector spaces(briefly TV spaces), but are not Serstnev PN spaces. We present a characterization of those PN spaces, whether they are TV spaces or not, in which the equivalence holds. Then a charaterization of the Archimedeanity of triangle functions \tau^* of type \tau_{T,L} is given.This work is a partial solution to a problema of comparing the concepts of distributional boundedness (D-bounded in short) and that of boundedness in the sense of associated strong topology

A study of boundedness in probabilistic normed spaces

Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity