On the Hitting Probability of Max-Stable Processes

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Hofmann, Martin; (2012)
  • Subject: 60G70 | Mathematics - Probability

The probability that a max-stable process {\eta} 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 {\eta} are comp... View more
  • References (6)

    1 − P (ηt 6= x, f.a. t ∈ [0, 1]) 1 − [P (ηt > x, f.a. t ∈ [0, 1]) + P (ηt < x, f.a. t ∈ [0, 1])] Ye d + (1 − Ye )e .

    a − 1 a − b [1] L. de Haan, A. Ferreira, Extreme Value Theory: An Introduction, Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006.

    [2] E. Gin´e, M. Hahn, P. Vatan, Max-infinitely divisible and max-stable sample continuous processes, Probab. Th. Rel. Fields 87 (2) (1990) 139-165.

    [3] S. Aulbach, M. Falk, M. Hofmann, On max-stable processes and the functional D-norm, Tech. rep., University of Wu¨rzburg, submitted (2012).

    [4] R. Takahashi, Characterizations of a multivariate extreme value distribution, Adv. Appl. Prob. 20 (1) (1988) 235-236.

    University of Wu¨rzburg, Institute of Mathematics, Emil-Fischer-Str. 30, 97074 Wu¨rzburg, Germany hofmann.martin@mathematik.uni-wuerzburg.de

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