Abstract
The probability that a max-stable process η in C[0, 1] with identical marginal distribution function F hits x \in R with 0 < F (x) < 1 is the hitting probability of x. We show that the hitting probability is always positive, unless the components of η are completely dependent. Moreover, we consider the event that the paths of standard MSP hit some x \in R twice and we give a sufficient condition for a positive probability of this event.
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