Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 1, Pages 9–26
DOI: https://doi.org/10.33048/semi.2021.18.002
(Mi semr1343)
 

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
Full-text PDF (435 kB) Citations (2)
References:
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.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-12007
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.3., проект № 0314-2019-0008
Received November 20, 2020, published January 12, 2021
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60F17
Language: Russian
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
Citation in format AMSBIB
\Bibitem{SakWacPro21}
\by A.~I.~Sakhanenko, V.~I.~Wachtel, E.~I.~Prokopenko, A.~D.~Shelepova
\paper On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 9--26
\mathnet{http://mi.mathnet.ru/semr1343}
\crossref{https://doi.org/10.33048/semi.2021.18.002}
Linking options:
  • https://www.mathnet.ru/eng/semr1343
  • https://www.mathnet.ru/eng/semr/v18/i1/p9
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024