Fractal Measures with Uniform Marginals
نویسندگان
چکیده
We provide several constructions of self-affine probability measures on the unit square with uniform marginals. These constructions include and extend constructions of previous authors and are parameterized in a natural way. In addition, for each different construction we determine the dimension of the parameter space and thus the level of flexibility (for instance, for approximation purposes) each construction allows. Finally, we give some simple approximation results showing how to approximate any measure with uniform marginals on the unit square with a fractal measure resulting from one of our constructions. Iterated function systems, self-affine measures, uniform marginals, copulas
منابع مشابه
Gaussian Marginals of Probability Measures with Geometric Symmetries
Let K be a convex body in the Euclidean space Rn, n ≥ 2, equipped with its standard inner product 〈·, ·〉 and Euclidean norm | · |. Consider K as a probability space equipped with its uniform (normalized Lebesgue) measure μ. We are interested in k-dimensional marginals of μ, that is, the push-forward μ◦P−1 E of μ by the orthogonal projection PE onto a k-dimensional subspace E ⊂ Rn. The question ...
متن کاملAnalysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension
Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...
متن کاملIndependent Marginals of Operator Lévy’s Probability Measures on Finite Dimensional Vector Spaces
We find exponents of independent marginals of operator Lévy’s measures, and show that those measures which are convolutions of onedimensional factors are multivariate Lévy’s with the factors being Lévy’s too. A characterization of exponents of such measures is also given. Introduction. In this note we shall be concerned with independent marginals of operator Lévy’s measures on finite dimensiona...
متن کاملOn concordance measures and copulas with fractal support
Copulas can be used to describe multivariate dependence structures. We explore the rôle of copulas with fractal support in the study of association measures. 1 General introduction and motivation Copulas are of interest because they link joint distributions to their marginal distributions. Sklar [12] showed that, for any real-valued random variables X1 and X2 with joint distribution H, there ex...
متن کاملUniform Probability
This paper develops a general theory of uniform probability for compact metric spaces. Special cases of uniform probability include Lebesgue measure, the volume element on a Riemannian manifold, Haar measure, and various fractal measures (all suitably normalized). This paper first appeared fall of 1990 in the Journal of Theoretical Probability, vol. 3, no. 4, pp. 611—626. The key words by which...
متن کامل