Estimates of the probability of a regenerative process reaching a high level

Kateryna Akbash; Ivan Matsak; Oleg Zakusylo

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arXiv · 2510.24600

Estimates of the probability of a regenerative process reaching a high level

Kateryna Akbash·Ivan Matsak·Oleg Zakusylo

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Abstract

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.

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Kateryna Akbash, Ivan Matsak, Oleg Zakusylo. 2025-10-28. Estimates of the probability of a regenerative process reaching a high level. https://arxiv.org/abs/2510.24600

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