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Recently, Durante and Jaworski (2008) [6] have proved that the class of absolutely continuous copulas with a given diagonal section is non-empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null-measure. In this paper, we show that if we consider sub-diagonals (or super-diagonals),(More)
We introduce a constructive method, by using a doubly stochastic measure, to describe all the copulas that, in view of Sklar’s Theorem, are able to connect a bivariate distribution to its marginals. We use this to give the lower and upper optimal bounds for all the copulas that extend a given subcopula.
In recent years special attention has been devoted to the problem of finding a copula, the diagonal section and opposite diagonal section of which are known. For given diagonal function and opposite diagonal functions, we provide necessary and sufficient conditions for the existence of a copula to have these functions as diagonal and opposite diagonal(More)
In this paper we study a class of duality functions given by the solution of a system of functional equations related to the De Rham system. With the aid of a generalized dyadic representation system in the unit interval, we study a negation N which is a duality function for pairs of operators satisfying certain boundary conditions. New properties of N are(More)
Taylor’s polynomial is a central tool in any elementary course in mathematical analysis. Nowadays, its importance is centred on its applications, for instance, to asymptotic analysis or to obtain satisfactory numerical or integral inequalities see, e.g., 1–5 . The core of these results comes from manipulations on the explicit formula of the remainder, that(More)
The aim of this paper is to show, using some of Barnsley’s ideas, how it is possible to generalize a fractal interpolation problem to certain post critically finite (PCF) compact sets in R. We use harmonic functions to solve this fractal interpolation problem. © 2013 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 28A78; 58E20
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