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Displaying similar documents to “Siciak's extremal function in complex and real analysis”

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...

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.

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.