Displaying similar documents to “Dimensions of random recursive sets.”

The Beta(p,1) extensions of the random (uniform) Cantor sets

Dinis D. Pestana, Sandra M. Aleixo, J. Leonel Rocha (2009)

Discussiones Mathematicae Probability and Statistics

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Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal...

Optimal transportation for multifractal random measures and applications

Rémi Rhodes, Vincent Vargas (2013)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.

On random fractals with infinite branching: definition, measurability, dimensions

Artemi Berlinkov (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

A note on correlation coefficient between random events

Czesław Stępniak (2015)

Discussiones Mathematicae Probability and Statistics

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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...