Large Deviation Inequalities for Noncommutative Martingales
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866913009223335936 |
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| author | Jiao, Yong Luo, Sijie Zhou, Dejian |
| author_facet | Jiao, Yong Luo, Sijie Zhou, Dejian |
| contents | We establish noncommutative analogs of some well-known large deviation inequalities for noncommutative random variables. Firstly, for the noncommutative independent case, we characterize the uniformly exponential integrability of random variables in terms of large deviation inequalities. Secondly, for noncommutative martingale differences, we establish two deviation inequalities according to the exponential integrability and $L_{p}$-boundedness of the martingale differences, respectively. Finally, we establish a noncommutative version of Gordin's decomposition, which enables us to derive a noncommutative ergodic theorem via deviation inequalities for noncommutative martingales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04935 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large Deviation Inequalities for Noncommutative Martingales Jiao, Yong Luo, Sijie Zhou, Dejian Operator Algebras Functional Analysis Probability 46L53, 46L52 We establish noncommutative analogs of some well-known large deviation inequalities for noncommutative random variables. Firstly, for the noncommutative independent case, we characterize the uniformly exponential integrability of random variables in terms of large deviation inequalities. Secondly, for noncommutative martingale differences, we establish two deviation inequalities according to the exponential integrability and $L_{p}$-boundedness of the martingale differences, respectively. Finally, we establish a noncommutative version of Gordin's decomposition, which enables us to derive a noncommutative ergodic theorem via deviation inequalities for noncommutative martingales. |
| title | Large Deviation Inequalities for Noncommutative Martingales |
| topic | Operator Algebras Functional Analysis Probability 46L53, 46L52 |
| url | https://arxiv.org/abs/2604.04935 |