Geodesic
On~the~time of~the~first level achievement for~the~ascending-descending process
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 86-94

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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 $\mathbf{E} N$ of the first achievement time a fixed level for trajectories of this process, including finding exact formulas for $\mathbf{E} N$, estimating from above with an inequality and obtaining the asymptotics of $\mathbf{E} N$ under an infinitely receding level.
Keywords: stochastic inventory control models, stochastic process, random walk, first passage time. 
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     author = {V. I. Lotov},
     title = {On~the~time of~the~first level achievement for~the~ascending-descending process},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {86--94},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a6/}
}
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V. I. Lotov. On~the~time of~the~first level achievement for~the~ascending-descending process. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 86-94. http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a6/