A characterization of mutual absolute continuity of probability measures on a filtered space
| Autor: | Mayer, Matthias Georg |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages |
| Databáze: | arXiv |
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