Hosts: prof. dr hab. Ryszard Szekli, prof. dr hab. Krzysztof Dębicki

Contact: dr Michał Krawiec (secretary), michal.krawiec at math.uni.wroc.pl

Current activity:

The seminar takes place once a week, on Thursdays from 12:15 - 14:00 in the form of a stationary meeting in room 603 (Mathematical Institute, UWr) or an online meeting on the Zoom platform. All current and more detailed information can be obtained from the seminar secretary.

Next seminar: 2023-11-09, 12:15 - 14:00

Pavel Ievlev (Université de Lausanne)

Extremes of multivariate locally-additive Gaussian random fields

Abstract:
In this talk, I am going to present some of my recent results in joint work with Nikolai Kriukiv on the extremes of multivariate Gaussian random fields. I will begin with the 2019 paper by K. Dębicki, E. Hashorva, and L. Wang, which laid the groundwork for further investigations in the area of multivariate Gaussian extremes. I will explain that some of the assumptions of this paper may not hold in cases that are practically important, and I will discuss how these issues can be amended by considering second-order contributions — I will clarify this terminology during the talk. Next, we will explore what is, in a sense, the simplest extension of these results from processes (indexed by R) to fields (indexed by R^n), which we refer to as 'locally-additive'. As an application of this extension, I will present an exact asymptotic result for the probability that a real-valued process first hits a high positive barrier and then a low negative barrier within a finite time horizon.