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

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).

arXiv admin note: substantial text overlap with arXiv:1208.6281

References in corpus (2)

• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
• A counterexample to a hypothesis of light tail of maximum distribution for continuous random processes with light finite-dimensional tails

Cited by in corpus (1)

• Discovering of boundedness and continuity of random fields by means of partition entropic scheme