

Principle Seminar of the Department of Probability Theory, Moscow State University
September 20, 2017 16:45, Moscow, MSU, auditorium 1224






Massive excursions of Gaussian random fields. Method of
moments
V. I. Piterbarg^{} ^{} Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
Asymptotic behavior of the probability of massive excursions above a high level
has been evaluated for Gaussian isotropic random fields with two times
a. s. differentiable trajectories. A massive excursion is an excursion which
base diameter exceeds a fixed number. In order to evaluate this asymptotic behavior,
a point process of exits out of a large domain is introduced for
Gaussian vector field which
components are copies of the initial field.
Then we study the moments of this point process.
As well, general results on rough (logarithmic) asymptotic
behavior of probabilities of high massive excursions are
obtained.

