Geodesic
On the asymptotics of the probability to stay above a non-increasing boundary for a non-homogeneous compound renewal process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1667-1688

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We consider a non-homogeneous compound renewal process, which is also known as a cumulative renewal process, or a continuous time random walk. We suppose that the jump sizes have zero means and finite variances, whereas the renewal-times has moments 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 homogeneous compound renewal process, due to A. Sakhanenko, V. Wachtel, E. Prokopenko, A. Shelepova (2021).
Keywords: compound renewal process, continuous time random walk, non-homogeneous process, boundary crossing problems, moving boundaries, exit times. 
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     author = {A. D. Shelepova and A. I. Sakhanenko},
     title = {On the asymptotics of the probability to stay above a non-increasing boundary for a non-homogeneous compound renewal process},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1667--1688},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a25/}
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A. D. Shelepova; A. I. Sakhanenko. On the asymptotics of the probability to stay above a non-increasing boundary for a non-homogeneous compound renewal process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1667-1688. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a25/