Constructions of fractal probability measures with uniform marginals
LE3 .A278 2015
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
Bivariate probability measures can be decomposed into their marginal distributions and their \copula," a cumulative distribution function of a bivariate measure with uniform marginals which encodes the underlying dependence structure between the variables. In certain circumstances, these copulas can be fractal or self-similar in nature, and to model these we desire parameterized families of fractal measures with uniform marginals. We discuss a known construction for such a family and provide two new constructions. We also examine the dimension of the parameter space for each construction in order to assess their ability to approximate a given measure.
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