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 
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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     author = {S. S. Rasova and B. P. Harlamov},
     title = {Non-decreasing continuous {semi-Markov} processes: asymptotics and asymmetry},
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     volume = {412},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_412_a11/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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