A representation theorem for set-valued submartingales
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929199071100928 |
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| author | Tuyen, Luc Tri Luan, Vu Thai |
| author_facet | Tuyen, Luc Tri Luan, Vu Thai |
| contents | The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales.
We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04006 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A representation theorem for set-valued submartingales Tuyen, Luc Tri Luan, Vu Thai Probability The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales. |
| title | A representation theorem for set-valued submartingales |
| topic | Probability |
| url | https://arxiv.org/abs/2312.04006 |