Monotone additive statistics on heavy-tailed convolution semigroups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866915900123250688 |
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| author | Fritz, Tobias Mu, Xiaosheng Tamuz, Omer |
| author_facet | Fritz, Tobias Mu, Xiaosheng Tamuz, Omer |
| contents | We study sub-semigroups of the semigroup of probability measures on $\mathbb{R}$ and monotone additive statistics on them, by which we mean maps to the reals that are monotone with respect to the stochastic order and additive under convolution. We show that scalar multiples of the expectation are the unique monotone additive statistics on the semigroup of measures with finite $p$-th moment, for any $1 \le p < \infty$. We also prove that the entire semigroup of probability measures admits no non-zero monotone additive statistic at all. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_01733 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Monotone additive statistics on heavy-tailed convolution semigroups Fritz, Tobias Mu, Xiaosheng Tamuz, Omer Probability Primary: 60E15. Secondary: 06F05 We study sub-semigroups of the semigroup of probability measures on $\mathbb{R}$ and monotone additive statistics on them, by which we mean maps to the reals that are monotone with respect to the stochastic order and additive under convolution. We show that scalar multiples of the expectation are the unique monotone additive statistics on the semigroup of measures with finite $p$-th moment, for any $1 \le p < \infty$. We also prove that the entire semigroup of probability measures admits no non-zero monotone additive statistic at all. |
| title | Monotone additive statistics on heavy-tailed convolution semigroups |
| topic | Probability Primary: 60E15. Secondary: 06F05 |
| url | https://arxiv.org/abs/1912.01733 |