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Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

  • Anders Rønn-Nielsen (a1) and Eva B. Vedel Jensen (a2)
Abstract

We consider a continuous, infinitely divisible random field in ℝ d , d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

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Corresponding author
* Postal address: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, DK-2000 Frederiksberg, Denmark. Email address: aro.fi@cbs.dk
** Postal address: Department of Mathematics and Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark. Email address: eva@imf.au.dk
References
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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