Distributional and Extremal Behaviour of Brownian Motion with Exponential Resetting
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866912953865863168 |
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| author | Dębicki, Krzysztof Hashorva, Enkelejd Michna, Zbigniew |
| author_facet | Dębicki, Krzysztof Hashorva, Enkelejd Michna, Zbigniew |
| contents | We study the distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting. We obtain an explicit renewal-type formula for the distribution of the supremum and then derive an approximation for its survival function. Moreover, we find the asymptotics of the tail distribution of the infimum. We also consider the stationary case and give a new explicit expression for the fidi's of such processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03050 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributional and Extremal Behaviour of Brownian Motion with Exponential Resetting Dębicki, Krzysztof Hashorva, Enkelejd Michna, Zbigniew Probability We study the distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting. We obtain an explicit renewal-type formula for the distribution of the supremum and then derive an approximation for its survival function. Moreover, we find the asymptotics of the tail distribution of the infimum. We also consider the stationary case and give a new explicit expression for the fidi's of such processes. |
| title | Distributional and Extremal Behaviour of Brownian Motion with Exponential Resetting |
| topic | Probability |
| url | https://arxiv.org/abs/2603.03050 |