V. I. Lotov, V. R. Khodzhibaev, “Inequalities in a two-sided boundary crossing problem for stochastic processes”, Sibirsk. Mat. Zh., 2021, Volume 62, Number 3,Pages <nobr>563

This article is cited in 2 papers

Inequalities in a two-sided boundary crossing problem for stochastic processes

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

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia
^c Namangan Engineering Construction Institute, Namangan, Uzbekistan
^d Institute of Mathematics, Namangan Regional Department, Uzbekistan Academy of Sciences, Namangan, Uzbekistan

Abstract: Considering a stationary stochastic process with independent increments (Lévy process), we study the probability of the first exit from a strip through its upper boundary. We find the two-sided inequalities for this probability under various conditions on the process.

Keywords: stationary stochastic process with independent increments, first exit time, boundary crossing problem, ruin probability.

UDC: 519.21

Received: 08.09.2020
Revised: 08.09.2020
Accepted: 18.11.2020

DOI: 10.33048/smzh.2021.62.308