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Principle Seminar of the Department of Probability Theory, Moscow State University
April 13, 2016 16:45, Moscow, MSU, auditorium 12-24

High extrema of Gaussian chaos processes

V. I. Piterbarg

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let $\xi(t)$ be a Gaussian stationary vector process. Let $g : R^d \rightarrow R$ be a homogeneous function of positive index. We study probabilities of large extrema of the Gaussian chaos process $g(\xi(t))$. Important examples include products of Gaussian processes and quadratic forms of them. We review existing results partially obtained in collaboration with E. Hashorva, D. Korshunov, and A. Zhdanov. We also present the principal methods of our investigations which are the Laplace asymptotic method and other asymptotic methods for probabilities of high excursions of Gaussian vector process' trajectories.