On the Time of the First Achievement of a Level by an Ascending–Descending Process

On the Time of the First Achievement of a Level by an Ascending–Descending Process Full article

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2023, Volume: 17, Number: 3, Pages: 592-599 Pages count : 8 DOI: 10.1134/s1990478923030122

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0010

We consider a stochastic process whose trajectories are characterized by alternate linear growth and linear decrease over time intervals of random length, while the process can also maintain its value unchanged for random periods of time between growth and decrease. This process can be considered as a mathematical model of accumulation and consumption of materials, where random periods of time for accumulation, consumption, and interruptions in operation are combined. We study the mean value EN of the time of first achievement of a fixed level by trajectories of this process, including finding exact formulas for EN, producing an upper bound in the form of an inequality, and obtaining the asymptotics of EN under the conditions of an infinitely receding level.

Lotov V.I.
On the Time of the First Achievement of a Level by an Ascending–Descending Process
Journal of Applied and Industrial Mathematics. 2023. V.17. N3. P.592-599. DOI: 10.1134/s1990478923030122 Scopus РИНЦ OpenAlex

Лотов В.И.
О времени первого достижения уровня для процесса возрастания-убывания
Сибирский журнал индустриальной математики. 2023. Т.26. №3. С.86–94. DOI: 10.33048/SIBJIM.2023.26.307 РИНЦ

Submitted:	Feb 21, 2023
Accepted:	Apr 27, 2023
Published print:	Nov 3, 2023
Published online:	Nov 3, 2023

Scopus:	2-s2.0-85175786843
Elibrary:	63823528
OpenAlex:	W4388337374

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