A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values

Ph. Barbe; Miriam Isabel Seifert

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arXiv · 1311.0540

A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values

Ph. Barbe·Miriam Isabel Seifert

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Abstract

We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to infinity. As a consequence, we derive conditional limit theorems for random pairs (X,Y)=(Ru(T),Rv(T)) given that X is large. These results imply earlier ones which were obtained in the literature under stronger assumptions.

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Ph. Barbe, Miriam Isabel Seifert. 2013-11-03. A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values. https://arxiv.org/abs/1311.0540

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