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

Kontakt: dr Michał Krawiec (sekretarz), michal.krawiec at math.uni.wroc.pl

For English version please see: English version.

Aktualna działalność:

Seminarium odbywa się raz w tygodniu, w czwartki w godz. 12:15 - 14:00 stacjonarnie w sali 603 lub w formie wideokonferencji na platformie Zoom. Wszystkie aktualne i bardziej szczegółowe informacje można uzyskać u sekretarza seminarium. Pełen wykaz zaplanowanych referatów znajduje się w zakładce Referaty.

Najbliższy referat: 2023-11-09, 12:15 - 14:00

Pavel Ievlev (Université de Lausanne)

Extremes of multivariate locally-additive Gaussian random fields

Streszczenie:
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.