The authors consider a nondecreasing continuous random process for which a family of the first hitting times for levels x > 0 forms a Lévy process with positive increments. For a class of such processes with Lévy density e −u/u α, 1 ≤ α < 2, asymptotics of the first three moments of their one-dimensional distributions as t goes to infinity are derived. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 412, 2013, pp. 227–236.
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Rasova, S.S., Harlamov, B.P. Nondecreasing Continuous Semi-Markov Processes: Asymptotics and Asymmetry. J Math Sci 204, 148–154 (2015). https://doi.org/10.1007/s10958-014-2193-4
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DOI: https://doi.org/10.1007/s10958-014-2193-4