Geodesic
On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 9-26.

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We consider a compound renewal process, which is also known as a cumulative renewal process, or a continuous time random walk. We suppose that the jump size has zero mean and finite variance, whereas the renewal-time has a moment of order greater than $3/2$. We investigate the asymptotic behaviour of the probability that this process is staying above a moving non-increasing boundary up to time $T$ which tends to infinity. Our main result is a generalization of a similar one for ordinary random walks obtained earlier by Denisov D., Sakhanenko A. and Wachtel V. in Ann. Probab., 2018.
Keywords: compound renewal process, continuous time random walk, boundary crossing problems, moving boundaries, exit times. 
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A. I. Sakhanenko; V. I. Wachtel; E. I. Prokopenko; A. D. Shelepova. On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 9-26. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a9/

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