Actuarial Seminar: Vitalii Makogin (University of Ulm, Germany)

The talk is dedicated to exploring limiting distributions for integral functionals applied to transformed (subordinated) Gaussian random fields. Moreover, we consider the general non-stationary Gaussian random fields, including stationary and anisotropic special cases. Particular attention is given to the volumes of excursion sets with results obtained through the Hermite expansion technique. Key contributions to the theory of limit theorems for random fields include:
 - A Gaussian limit for volumes of excursion sets of long-range dependent random fields is proved with the normalization different from CLT under the short-range dependence.
- The limit theorems under long-range dependence are extended to the non-stationary Gaussian random fields. Moreover, integration domains now grow in the van Hove sense, which allows for more flexibility in their geometry.
- The subordination allows getting the limit theorems for the class of random fields with infinite variance.

Seminar organized by Prof. Enkelejd Hashorva