Mean residual life processes and associated submartingales
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866908586423091200 |
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| author | Bogso, Antoine-Marie |
| author_facet | Bogso, Antoine-Marie |
| contents | We use Madan-Yor's argument to construct associated submartingales to a class of two-parameter processes that are ordered by the increasing convex dominance. This class includes processes which have MTP$_2$ integrated survival functions. We prove that the integrated survival function of an integrable two-parameter process is MTP$_2$ if and only if it is TP$_2$ in each pair of arguments when the remaining argument is fixed. This result can not be deduced from known results since there are several two-parameter processes whose integrated survival functions do not have interval support. The MTP$_2$ property of certain MRL processes is useful to exhibit numerous other processes having the same property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_05932 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Mean residual life processes and associated submartingales Bogso, Antoine-Marie Probability 60E15, 60G44, 60J25 We use Madan-Yor's argument to construct associated submartingales to a class of two-parameter processes that are ordered by the increasing convex dominance. This class includes processes which have MTP$_2$ integrated survival functions. We prove that the integrated survival function of an integrable two-parameter process is MTP$_2$ if and only if it is TP$_2$ in each pair of arguments when the remaining argument is fixed. This result can not be deduced from known results since there are several two-parameter processes whose integrated survival functions do not have interval support. The MTP$_2$ property of certain MRL processes is useful to exhibit numerous other processes having the same property. |
| title | Mean residual life processes and associated submartingales |
| topic | Probability 60E15, 60G44, 60J25 |
| url | https://arxiv.org/abs/1807.05932 |