Estimates of the probability of a regenerative process reaching a high level
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911236930666496 |
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| author | Akbash, Kateryna Matsak, Ivan Zakusylo, Oleg |
| author_facet | Akbash, Kateryna Matsak, Ivan Zakusylo, Oleg |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates of the probability of a regenerative process reaching a high level Akbash, Kateryna Matsak, Ivan Zakusylo, Oleg Probability 60K25, 60F05 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. |
| title | Estimates of the probability of a regenerative process reaching a high level |
| topic | Probability 60K25, 60F05 |
| url | https://arxiv.org/abs/2510.24600 |