V. I. Lotov, “Properties of boundary functionals for a random walk with stable jump distributions”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 455

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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 1, Pages 455–464
DOI: https://doi.org/10.33048/semi.2023.20.026 (Mi semr1590)

Probability theory and mathematical statistics

Properties of boundary functionals for a random walk with stable jump distributions

V. I. Lotov

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

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DOI: https://doi.org/10.33048/semi.2023.20.026

Abstract: For a random walk with jumps having strictly stable distributions, we obtain theorems that characterize properties of ladder epochs and ladder heights. We also give exact expressions for the distribution of the sojourn time of the random walk trajectory on the positive semi-axis for a finite number of steps.

Keywords: random walk, ladder epoch, ladder height, strictly stable distribution, sojourn time on the semi-axis.

Funding agency	Grant number
Ministry of Science and Higher Education of the Russian Federation	FWNF-2022-0010

Received January 18, 2023, published July 3, 2023

Document Type: Article

UDC: 519.21

MSC: 60G50

Language: Russian

Citation: V. I. Lotov, “Properties of boundary functionals for a random walk with stable jump distributions”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 455–464

Citation in format AMSBIB

\Bibitem{Lot23}

\by V.~I.~Lotov

\paper Properties of boundary functionals for a random walk with stable jump distributions

\jour Sib. \`Elektron. Mat. Izv.

\yr 2023

\vol 20

\issue 1

\pages 455--464

\mathnet{http://mi.mathnet.ru/semr1590}

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https://www.mathnet.ru/eng/semr/v20/i1/p455

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