2025/10/28 by Akbash, Kateryna, Matsak, Ivan, Zakusylo, Oleg
#60F05 #60K25 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2510.24600
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary results for geometric sums with delay will play an important role. Examples of application to random processes describing queue lengths in queueing theory are also given.