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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18555 |
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Table of 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.