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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2411.18555 |
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| _version_ | 1866913588652802048 |
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| author | Mayer, Matthias Georg |
| author_facet | Mayer, Matthias Georg |
| contents | We give a new characterization for mutual absolute continuity of probability measures on a filtered space. For this, we introduce a martingale limit $M$ that measures the similarity between the tails of the probability measures restricted to the filtration. The measures are mutually absolutely continuous if and only if $M = 1$ holds almost surely for both measures. In this case, the square roots of the Radon-Nikodym derivatives on the filtration converge in $L^2$. Finally, we apply the result to families of random variables and stochastic processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of mutual absolute continuity of probability measures on a filtered space Mayer, Matthias Georg Probability 60G (Primary) 60B10 (Secondary) We give a new characterization for mutual absolute continuity of probability measures on a filtered space. For this, we introduce a martingale limit $M$ that measures the similarity between the tails of the probability measures restricted to the filtration. The measures are mutually absolutely continuous if and only if $M = 1$ holds almost surely for both measures. In this case, the square roots of the Radon-Nikodym derivatives on the filtration converge in $L^2$. Finally, we apply the result to families of random variables and stochastic processes. |
| title | A characterization of mutual absolute continuity of probability measures on a filtered space |
| topic | Probability 60G (Primary) 60B10 (Secondary) |
| url | https://arxiv.org/abs/2411.18555 |