Sharp estimates on the tail behavior of a multistable distribution

Antoine Ayache

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arXiv · 1208.0911

Sharp estimates on the tail behavior of a multistable distribution

Antoine Ayache

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Abstract

Multistable distributions, which have been introduced recently by Falconer, Lévy Véhel and their co-authors, are natural generalizations of symmetric "alpha" stable distributions; roughly speaking, they are obtained by replacing the constant parameter "alpha" by a (Lebesgue) mesurable function. It is known that the tail of a symmetric "alpha" stable distribution asymptotically behaves as a power function with exponent "-alpha"; in this article we extend the latter result to the setting of multistable distributions.

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Antoine Ayache. 2012-08-04. Sharp estimates on the tail behavior of a multistable distribution. https://arxiv.org/abs/1208.0911

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