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ОБ АСИМПТОТИКЕ РАСПРЕДЕЛЕНИЯ МОМЕНТА ВЫХОДА ОБОБЩЕННОГО ПРОЦЕССА ВОССТАНОВЛЕНИЯ ЗА НЕВОЗРАСТАЮЩУЮ ГРАНИЦУ Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2021, Volume: 18, Number: 1, Pages: 9-26 Pages count : 18 DOI: 10.33048/semi.2021.18.002
Tags boundary crossing problems; compound renewal process; continuous time random walk; exit times; moving boundaries
Authors Sakhanenko A. 1 , Wachtel V. 2 , Prokopenko E. 1 , Shelepova A. 3
Affiliations
1 Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russian Federation
2 Universität Augsburg, Institut fur Mathematik, Augsburg, 86135, Germany
3 Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russian Federation

Funding (2)

1 Russian Foundation for Basic Research 20-51-12007
2 Sobolev Institute of Mathematics 0314-2019-0008

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. © 2021 Саханенко А.И., Вахтель В.И., Прокопенко Е.И., Шелепова А.Д. All Rights Reserved.
Cite: Sakhanenko A. , Wachtel V. , Prokopenko E. , Shelepova A.
ОБ АСИМПТОТИКЕ РАСПРЕДЕЛЕНИЯ МОМЕНТА ВЫХОДА ОБОБЩЕННОГО ПРОЦЕССА ВОССТАНОВЛЕНИЯ ЗА НЕВОЗРАСТАЮЩУЮ ГРАНИЦУ
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2021. V.18. N1. P.9-26. DOI: 10.33048/semi.2021.18.002 WOS Scopus OpenAlex
Identifiers:
Web of science: WOS:000616344300001
Scopus: 2-s2.0-85108805473
OpenAlex: W3199071530
Citing:
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Scopus 2
OpenAlex 1
Web of science 1
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