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.
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Funding
V. I. Lotov was partially supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.3, Project 0314–2016–0008).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 567–575. https://doi.org/10.33048/smzh.2021.62.308
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Lotov, V.I., Khodjibayev, V.R. Inequalities in a Two-Sided Boundary Crossing Problem for Stochastic Processes. Sib Math J 62, 455–461 (2021). https://doi.org/10.1134/S0037446621030083
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DOI: https://doi.org/10.1134/S0037446621030083
Keywords
- stationary stochastic process with independent increments
- first exit time
- boundary crossing problem
- ruin probability