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Displaying similar documents to “Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties”

The Siciak-Zahariuta extremal function as the envelope of disc functionals

Finnur Lárusson, Ragnar Sigurdsson (2005)

Annales Polonici Mathematici

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We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. This function is also known as the pluricomplex Green function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert's formula for this function from the convex case to the connected case.

Estimating the extremal index through the tail dependence concept

Marta Ferreira (2015)

Discussiones Mathematicae Probability and Statistics

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The extremal index Θ is an important parameter in extreme value analysis when extending results from independent and identically distributed sequences to stationary ones. A connection between the extremal index and the tail dependence coefficient allows the introduction of new estimators. The proposed ones are easy to compute and we analyze their performance through a simulation study. Comparisons with other existing methods are also presented. Case studies within environment are considered...

Siciak-Zahariuta extremal functions and polynomial hulls

Finnur Lárusson, Ragnar Sigurdsson (2007)

Annales Polonici Mathematici

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We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.