V. I. Lotov, V. R. Khodzhibaev, “Inequalities for the average first exit time from the strip for the Levy process”, Sib. Èlektron. Mat. Izv., 2022, Volume 19, Issue 2,Pages <nobr>852

Probability theory and mathematical statistics

Inequalities for the average first exit time from the strip for the Levy process

V. I. Lotov^ab, V. R. Khodzhibaev^cd

^a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia
^c Institute of Mathematics Uzbekistan Akademy of Sciences, Universitetskaya str., 46, 100174, Tashkent, Uzbekistan
^d Namangan Engineering - construction Institute, Islam Karimov str., 12, 160103, Namangan, Uzbekistan

Abstract: We study first exit time from a strip for a homogeneous stochastic process with independent increments (the Levy process). Two-sided inequalities are found for the average of this exit time under various conditions on the process.

Keywords: stochastic Levy process, first exit time, boundary crossing problem, ruin probability.

UDC: 519.21

MSC: 60G50

Received July 25, 2022, published November 11, 2022

DOI: 10.33048/semi.2022.19.071