An abstract decomposition of measures and its many applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914115458433024 |
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| author | Milazzo, Alessandro Siorpaes, Pietro |
| author_facet | Milazzo, Alessandro Siorpaes, Pietro |
| contents | We consider a little-known abstract decomposition result for positive measures due to Dellacherie, and show that it yields many decompositions of measures, several of which are new. We then extend Dellacherie's result to (controlled) vector measures, and apply it to obtain a decomposition of semimartingales due to Bichteler, on which we improve. Then, we investigate how the outputs of the decomposition depend on its inputs, in particular characterising the two elements of the decomposition as projections in the sense of Riesz spaces and of metric spaces. Finally, we prove a decomposition theorem for strictly positive operators on Riesz spaces which generalises Dellacherie's Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_07487 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An abstract decomposition of measures and its many applications Milazzo, Alessandro Siorpaes, Pietro Probability 28A33, 28B05, 46G10, 47B15 We consider a little-known abstract decomposition result for positive measures due to Dellacherie, and show that it yields many decompositions of measures, several of which are new. We then extend Dellacherie's result to (controlled) vector measures, and apply it to obtain a decomposition of semimartingales due to Bichteler, on which we improve. Then, we investigate how the outputs of the decomposition depend on its inputs, in particular characterising the two elements of the decomposition as projections in the sense of Riesz spaces and of metric spaces. Finally, we prove a decomposition theorem for strictly positive operators on Riesz spaces which generalises Dellacherie's Theorem. |
| title | An abstract decomposition of measures and its many applications |
| topic | Probability 28A33, 28B05, 46G10, 47B15 |
| url | https://arxiv.org/abs/2204.07487 |