Об асимптотике распределения момента выхода обобщенного процесса восстановления за невозрастающую границу

Translated title of the contribution: On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process

Alexander Sakhanenko, Vitali Wachtel, Evgeny Prokopenko, Anastasiya Shelepova

Research output: Contribution to journalArticlepeer-review

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.

Translated title of the contributionOn the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
Original languageRussian
Article number2
Pages (from-to)9-26
Number of pages18
JournalSiberian Electronic Mathematical Reports
Volume18
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • boundary crossing problems
  • compound renewal process
  • continuous time random walk
  • exit times
  • moving boundaries

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27.43 Probability Theory and mathematical statistics

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