Allowing for imprecision in the game-theoretic characterisation of the Poisson process
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914436926668800 |
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| author | Erreygers, Alexander |
| author_facet | Erreygers, Alexander |
| contents | In their 1993 paper 'Forecasting point and continuous processes: Prequential analysis' in Test, Vovk put forward a game-theoretic definition of the Poisson process. A key assumption therein is that the rate of the Poisson process is known or specified exactly. In contrast, I replace this assumption with the less stringent -- and arguably more realistic -- one that the available information about the process takes the form of bounds on the rate rather than a single, exact value. The resulting process has properties similar to the standard, 'precise' Poisson process, albeit with an imprecise flavour to them, thus justifying the moniker 'imprecise Poisson process'. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Allowing for imprecision in the game-theoretic characterisation of the Poisson process Erreygers, Alexander Probability 60G65 (Primary) 60G55 (Secondary) In their 1993 paper 'Forecasting point and continuous processes: Prequential analysis' in Test, Vovk put forward a game-theoretic definition of the Poisson process. A key assumption therein is that the rate of the Poisson process is known or specified exactly. In contrast, I replace this assumption with the less stringent -- and arguably more realistic -- one that the available information about the process takes the form of bounds on the rate rather than a single, exact value. The resulting process has properties similar to the standard, 'precise' Poisson process, albeit with an imprecise flavour to them, thus justifying the moniker 'imprecise Poisson process'. |
| title | Allowing for imprecision in the game-theoretic characterisation of the Poisson process |
| topic | Probability 60G65 (Primary) 60G55 (Secondary) |
| url | https://arxiv.org/abs/2604.00598 |