Geodesic
Non-decreasing continuous semi-Markov processes: asymptotics and asymmetry
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 227-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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The authors consider a non-decreasing continuous random process with a family of the first hitting times for levels $x>0$, which form Lévy process with positive increments. Asymptotics of the first three moments of their one-dimensional distributions as t goes to infinity are derived for the case when the Lévy density is $e^{-u}/u^\alpha$ $(1\leq\alpha<2)$. 
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S. S. Rasova; B. P. Harlamov. Non-decreasing continuous semi-Markov processes: asymptotics and asymmetry. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 19, Tome 412 (2013), pp. 227-236. http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a11/

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