Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Sonderveranstaltung Mini-Course

 

Professor Dr. D. Korshunov
Lancester University, U.K.

 
spricht am
 
Mittwoch, 28. Juni 2017
 
um
 
16:00 Uhr
 
im
 
Raum 2006 (L1)
 
über das Thema:
 

»Asymptotic tail analysis of Gaussian chaos and Shepp statistics«

Abstract:
We discuss various methods of asymptotic analysis of tail distribution in some Gaussian models. The first model is the Gaussian chaos, that is, a homogeneous polynomial (or, more generally, a homogeneous function) of a standard normal vector. The simplest case is given by the product of components of a normal random vector with a general covariance matrix, more complicated functionals are given by some characteristics of the Gaussian orthogonal ensemble. We explain how to show that the distribution of the Gaussian chaos is usually heavy-tailed, via a direct probabilistic approach and via the Laplace method. The second model is the Shepp statistics which is defined as the maximium of increments of the Brownian motion. Firstly we discuss tail asymptotics of the Shepp statistics in one-dimensional case and then proceed to multi-dimensional processes. This Mini-Course consists of three days: 28.06./12.07./19.07.2017.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Vitali Wachtel



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