Extremes of Gaussian chaos processes with trend.

Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca: 
Long Bai (University of Lausanne)
Data spotkania seminaryjnego: 
czwartek, 4. Styczeń 2018 - 12:15
Let X(t) = (X_1(t), . . . , X_d(t)) be a Gaussian vector process and g(x), x ∈ R_d a homogenous function. In this paper we are concerned with the exact tail asymptotics of the chaos process g(X(t)) with trend over [0, S]. Both scenarios that X(t) is locally stationary and non-stationary are considered. Important examples include Π^d_{i=1} X_i(t) − ct and chi-processes with trend, i.e., (\sum^d_{i=1} b_i X^2_i(t) )− ct. Based on joint work with Enkelejd Hashorva and Dmitry Korshunov.