Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process

Bikramjit Das; Sebastian Engelke; Enkelejd Hashorva

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arXiv · 1311.3409

Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process

Bikramjit Das·Sebastian Engelke·Enkelejd Hashorva

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Abstract

The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown-Resnick process is well-known in the literature. In this paper, we study the extremal functional behavior of non-Gaussian processes, namely squared Bessel processes and scalar products of Brownian motions. It is shown that maxima of independent samples of those processes converge weakly on the space of continuous functions to the Brown-Resnick process.

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Bikramjit Das, Sebastian Engelke, Enkelejd Hashorva. 2013-11-14. Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process. https://arxiv.org/abs/1311.3409

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