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.
- Convolution equivalence
- Excursion set
- Infinite divisibility
- Lévy-based modelling
Rønn-Nielsen, A., & Jensen, E. B. V. (2017). Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure. Journal of Applied Probability, 54(3), 833-851. https://doi.org/10.1017/jpr.2017.37