Moderate, large and super large deviations principles for Poisson process with uniform catastrophes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913862703382528 |
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| author | Logachov, A. Logachova, O. Yambartsev, A. |
| author_facet | Logachov, A. Logachova, O. Yambartsev, A. |
| contents | In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear (moderate deviations), linear (large deviations), and superlinear (superlarge deviations). Across these scales, we establish different yet coherent rate functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moderate, large and super large deviations principles for Poisson process with uniform catastrophes Logachov, A. Logachova, O. Yambartsev, A. Probability 60F10, 60J27 In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear (moderate deviations), linear (large deviations), and superlinear (superlarge deviations). Across these scales, we establish different yet coherent rate functions. |
| title | Moderate, large and super large deviations principles for Poisson process with uniform catastrophes |
| topic | Probability 60F10, 60J27 |
| url | https://arxiv.org/abs/2411.19255 |