Deviation inequalities for contractive infinite memory processes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917940694089728 |
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| author | Doukhan, Paul Fan, Xiequan |
| author_facet | Doukhan, Paul Fan, Xiequan |
| contents | In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale decomposition method, we establish some deviation and moment inequalities for separately Lipschitz functions of such a process, under various moment conditions on some dominating random variables. Our results generalize the Markov models of Dedecker and Fan [Stochastic Process. Appl., 2015] and a recent paper by Chazottes et al. [Ann. Appl. Probab., 2023] for the special case of a specific class of infinite memory models with discrete values. An application to stochastic gradient Langevin dynamic algorithm is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deviation inequalities for contractive infinite memory processes Doukhan, Paul Fan, Xiequan Probability 60G42, 60J05, 60E15 In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale decomposition method, we establish some deviation and moment inequalities for separately Lipschitz functions of such a process, under various moment conditions on some dominating random variables. Our results generalize the Markov models of Dedecker and Fan [Stochastic Process. Appl., 2015] and a recent paper by Chazottes et al. [Ann. Appl. Probab., 2023] for the special case of a specific class of infinite memory models with discrete values. An application to stochastic gradient Langevin dynamic algorithm is also discussed. |
| title | Deviation inequalities for contractive infinite memory processes |
| topic | Probability 60G42, 60J05, 60E15 |
| url | https://arxiv.org/abs/2408.11719 |