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Name: Anders Ronn-Nielsen 

Talk Title: Extreme value theory for spatial random fields - with application to a Lévy-driven field

Abstract: First, we consider a stationary random field indexed by an increasing sequence of discrete sets of spatial grid points. Under certain mixing and anti-clustering conditions combined with a very broad assumption on how the sequence of spatial index sets increases, we obtain an extremal result that relates a normalized version of the distribution of the maximum of the field over the index sets to the tail distribution of the individual variables. Furthermore, we identify the limiting distribution as an extreme value distribution. Secondly, we consider a continuous, infinitely divisible spatial random field given as an integral of a kernel function with respect to a Lévy basis with a levy measure that is either of the following: convolution equivalent; regularly varying; subexponential and in the Gumbel domain of attraction. When observing the supremum of this field over an increasing sequence of (continuous) index sets, we obtain an extreme value theorem for the distribution of this supremum. The proof relies on discretization and a conditional version of the technique applied in the first part, as we condition on the high activity and light-tailed part of the field.

This talk is a contributed talk at EVA 2021. View the programme here.