Can the tail for maximum of continuous random field be significantly more heavy than maximum of tails?

Eugene Ostrovsky; Leonid Sirota

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arXiv · 1508.05646

Can the tail for maximum of continuous random field be significantly more heavy than maximum of tails?

Eugene Ostrovsky·Leonid Sirota

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Abstract

We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with (relatively) heavy tail of maximum distribution. The apparatus for tails comparison are embedding results for Orlicz and Grand Lebesgue Spaces (GLS).

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Eugene Ostrovsky, Leonid Sirota. 2015-08-23. Can the tail for maximum of continuous random field be significantly more heavy than maximum of tails?. https://arxiv.org/abs/1508.05646

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