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., 2023, Volume 20, Issue 2,Pages <nobr>1013

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. Lotov^a, V. R. Khodjibaev^bc

^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

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.

UDC: 519.21

MSC: 60G50

Received July 7, 2023, published November 12, 2023

DOI: doi.org/10.33048/semi.2023.20.062