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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2021_18_1_a9,
     author = {A. I. Sakhanenko and V. I. Wachtel and E. I. Prokopenko and A. D. Shelepova},
     title = {On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {9--26},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a9/}
}
TY  - JOUR
AU  - A. I. Sakhanenko
AU  - V. I. Wachtel
AU  - E. I. Prokopenko
AU  - A. D. Shelepova
TI  - On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 9
EP  - 26
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a9/
LA  - ru
ID  - SEMR_2021_18_1_a9
ER  - 
%0 Journal Article
%A A. I. Sakhanenko
%A V. I. Wachtel
%A E. I. Prokopenko
%A A. D. Shelepova
%T On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 9-26
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a9/
%G ru
%F SEMR_2021_18_1_a9
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/