### Abstract

We consider a continuous, infinitely divisible random field in Rd 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

supremum of the field exceeds the level x as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

supremum of the field exceeds the level x as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

Original language | English |
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Journal | Journal of Applied Probability |

Volume | 53 |

Issue number | 1 |

Pages (from-to) | 244–261 |

Number of pages | 18 |

ISSN | 0021-9002 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |

### Keywords

- Asymptotic supremum
- Convolution equivalence
- Infinite divisibility
- Lévybased modelling

### Cite this

Rønn-Nielsen, A., & Jensen, E. B. V. (2016). Tail Asymptotics for the Supremum of an Infinitely Divisible Field with Convolution Equivalent Lévy Measure.

*Journal of Applied Probability*,*53*(1), 244–261. https://doi.org/10.1017/jpr.2015.22