Short Communications

On the shape of high excursions of Gaussian stationary processes

E. V. Kremena

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study the form of excursions of a Gaussian stationary process intersecting a high level $u$. We show that the trajectories fluctuate in this case in a narrow tube around the expected motion. We also find an upper bound for the probability that the trajectory intersects the boundary of this tube as $u$ goes off to infinity.

Keywords: Gaussian processes, trajectory, excursion form, asymptotics of the high excursion probability.

Received: 19.09.2019
Accepted: 19.09.2019

DOI: 10.4213/tvp5346

 English version: Theory of Probability and its Applications, 2020, 65:1, 111–113

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