On a convergence of positive continuous additive functionals in terms of their smooth measures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910436694163456 |
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| author | Nishimori, Yasuhito Tomisaki, Matsuyo Tsuchida, Kaneharu Uemura, Toshihiro |
| author_facet | Nishimori, Yasuhito Tomisaki, Matsuyo Tsuchida, Kaneharu Uemura, Toshihiro |
| contents | A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric on the space of measures of finite energy integrals and show some structures of the metric. Then, we show the compactness and give some examples of positive continuous additive functionals that the convergence holds in terms of the associated smooth measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a convergence of positive continuous additive functionals in terms of their smooth measures Nishimori, Yasuhito Tomisaki, Matsuyo Tsuchida, Kaneharu Uemura, Toshihiro Probability 60J46, 31C25, 60F99 A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric on the space of measures of finite energy integrals and show some structures of the metric. Then, we show the compactness and give some examples of positive continuous additive functionals that the convergence holds in terms of the associated smooth measures. |
| title | On a convergence of positive continuous additive functionals in terms of their smooth measures |
| topic | Probability 60J46, 31C25, 60F99 |
| url | https://arxiv.org/abs/2405.03937 |