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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 1, Pages 138–141
DOI: https://doi.org/10.4213/tvp5346 (Mi tvp5346) 		 
Short Communications

On the shape of high excursions of Gaussian stationary processes

E. V. Kremena

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/tvp5346
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
English version:
Theory of Probability and its Applications, 2020, Volume 65, Issue 1, Pages 111–113
DOI: https://doi.org/10.1137/S0040585X97T989854
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. V. Kremena, “On the shape of high excursions of Gaussian stationary processes”, Teor. Veroyatnost. i Primenen., 65:1 (2020), 138–141; Theory Probab. Appl., 65:1 (2020), 111–113
Citation in format AMSBIB
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    • Citing articles in Google Scholar: Russian citations, English citations
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