Exponential inequalities for the supremum of some counting processes and their square martingales
We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors in statistical procedures, apply to general n...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.206/ |
| _version_ | 1797651576058281984 |
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| author | Le Guével, Ronan |
| author_facet | Le Guével, Ronan |
| author_sort | Le Guével, Ronan |
| collection | DOAJ |
| description | We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors in statistical procedures, apply to general non-explosive counting processes including Poisson, Hawkes and Cox models. Some applications for $U$-statistics are discussed. |
| first_indexed | 2024-03-11T16:16:45Z |
| format | Article |
| id | doaj.art-e6f1244ca36f4a59a95f5eefcbd375bb |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:45Z |
| publishDate | 2021-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-e6f1244ca36f4a59a95f5eefcbd375bb2023-10-24T14:19:20ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-10-01359896998210.5802/crmath.20610.5802/crmath.206Exponential inequalities for the supremum of some counting processes and their square martingalesLe Guével, Ronan0Université Rennes 2, France.We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors in statistical procedures, apply to general non-explosive counting processes including Poisson, Hawkes and Cox models. Some applications for $U$-statistics are discussed.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.206/ |
| spellingShingle | Le Guével, Ronan Exponential inequalities for the supremum of some counting processes and their square martingales Comptes Rendus. Mathématique |
| title | Exponential inequalities for the supremum of some counting processes and their square martingales |
| title_full | Exponential inequalities for the supremum of some counting processes and their square martingales |
| title_fullStr | Exponential inequalities for the supremum of some counting processes and their square martingales |
| title_full_unstemmed | Exponential inequalities for the supremum of some counting processes and their square martingales |
| title_short | Exponential inequalities for the supremum of some counting processes and their square martingales |
| title_sort | exponential inequalities for the supremum of some counting processes and their square martingales |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.206/ |
| work_keys_str_mv | AT leguevelronan exponentialinequalitiesforthesupremumofsomecountingprocessesandtheirsquaremartingales |