|
On the time of the first level achievement for the ascending-descending process
V. I. Lotov Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
Abstract:
We consider a stochastic process whose trajectories are characterized by alternate linear growth and linear decrease during time intervals of random length; the process can also keep its value during random intervals of time between growth and decrease. This process can be considered as a mathematical model of accumulation and consumption of materials, when random periods of time are combined for accumulation, spending and interruptions in operation. We study mean value EN of the first achievement time a fixed level for trajectories of this process, including finding exact formulas for EN, estimating from above with an inequality and obtaining the asymptotics of EN under an infinitely receding level.
Keywords:
stochastic inventory control models, stochastic process, random walk, first passage time.
Received: 21.02.2023 Revised: 01.03.2023 Accepted: 27.04.2023
Citation:
V. I. Lotov, “On the time of the first level achievement for the ascending-descending process”, Sib. Zh. Ind. Mat., 26:3 (2023), 86–94; J. Appl. Industr. Math., 17:3 (2023), 592–599
Linking options:
https://www.mathnet.ru/eng/sjim1249 https://www.mathnet.ru/eng/sjim/v26/i3/p86
|
Statistics & downloads: |
Abstract page: | 64 | Full-text PDF : | 16 | References: | 21 | First page: | 5 |
|