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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 1013–1025
DOI: https://doi.org/doi.org/10.33048/semi.2023.20.062 (Mi semr1625) 		 
Probability theory and mathematical statistics

On the distribution of the crossing number of a strip by trajectories of a stochastic process with independent increments

V. I. Lotova, V. R. Khodjibaevbc

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Namangan Engineering - construction Institute, Islam Karimov str., 12, 160103, Namangan, Uzbekistan
c Institute of Mathematics Uzbekistan Akademy of Sciences, Universitetskaya str., 46, 100174, Tashkent, Uzbekistan
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DOI: https://doi.org/doi.org/10.33048/semi.2023.20.062
Abstract: We study the distribution of the crossing number of a strip with straight parallel boundaries by trajectories of a stochastic process with independent increments (Levy process). For the distribution under study, we give a number of inequalities, as well as asymptotic representations for unlimitedly expanding strip.
Keywords: stationary stochastic process with independent increments (Levy process), number of strip crossings, probabilistic inequalities.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0010
Received July 7, 2023, published November 12, 2023
Document Type: Article
UDC: 519.21
MSC: 60G50
Language: Russian
Citation: V. I. Lotov, V. R. Khodjibaev, “On the distribution of the crossing number of a strip by trajectories of a stochastic process with independent increments”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1013–1025
Citation in format AMSBIB
\Bibitem{LotKho23}
\by V.~I.~Lotov, V.~R.~Khodjibaev
\paper On the distribution of the crossing number of a strip by trajectories of a stochastic process with independent increments
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 1013--1025
\mathnet{http://mi.mathnet.ru/semr1625}
\crossref{https://doi.org/doi.org/10.33048/semi.2023.20.062}
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