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This article is cited in 2 scientific papers (total in 2 papers)
Probability theory and mathematical statistics
On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
A. I. Sakhanenkoa, V. I. Wachtelb, E. I. Prokopenkoa, A. D. Shelepovac a Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
b Universität Augsburg, Institut für Mathematik, Augsburg, 86135, Germany
c Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Abstract:
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.
Received November 20, 2020, published January 12, 2021
Citation:
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”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 9–26
Linking options:
https://www.mathnet.ru/eng/semr1343 https://www.mathnet.ru/eng/semr/v18/i1/p9
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