Extremes of multivariate locally-additive Gaussian random fields

Ievlev Pavel, University of Lausanne

In this talk, I am going to present some of my recent results in joint work with Nikolai Kriukov 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.

Area: CS60 - Extreme value theory (Evgeny Spodarev)

Keywords: Gaussian processes, multivariate extremes, random fields

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