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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.03512 |
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| _version_ | 1866909411389210624 |
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| author | Huang, Wen Liu, Chunlin Peng, Shige Qu, Baoyou |
| author_facet | Huang, Wen Liu, Chunlin Peng, Shige Qu, Baoyou |
| contents | We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear expectation systems are ergodic, we derive stronger results. Furthermore, we relax the conditions for the law of large numbers and the strong law of large numbers under sublinear expectations from independent and identical distribution to $α$-mixing. These results can be applied to a class of stochastic differential equations driven by $G$-Brownian motion (i.e., $G$-SDEs), such as $G$-Ornstein-Uhlenbeck processes.
As byproducts, we also obtain a series of applications for classical ergodic theory and capacity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ergodicity and Mixing of Sublinear Expectation System and Applications Huang, Wen Liu, Chunlin Peng, Shige Qu, Baoyou Probability Primary 37A25, 60G65, secondary 28A12, 60F17 We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear expectation systems are ergodic, we derive stronger results. Furthermore, we relax the conditions for the law of large numbers and the strong law of large numbers under sublinear expectations from independent and identical distribution to $α$-mixing. These results can be applied to a class of stochastic differential equations driven by $G$-Brownian motion (i.e., $G$-SDEs), such as $G$-Ornstein-Uhlenbeck processes. As byproducts, we also obtain a series of applications for classical ergodic theory and capacity theory. |
| title | Ergodicity and Mixing of Sublinear Expectation System and Applications |
| topic | Probability Primary 37A25, 60G65, secondary 28A12, 60F17 |
| url | https://arxiv.org/abs/2411.03512 |