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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01045 |
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| _version_ | 1866917399153868800 |
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| author | Waymire, Edward C |
| author_facet | Waymire, Edward C |
| contents | In this note, the time reversible case of a general theorem of Bhattacharya is shown to imply the Kipnis-Varadhan functional central limit theorem for ergodic Markov processes. To this end, a few results from semigroup theory, including the resolvent identity, are incoporated in Bhattacharya's range condition for the inifinitesimal generator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes Waymire, Edward C Probability 60J25, 60F05, 60G44 (Primary) 47B02, 47B25, 47B93 (Secondary) In this note, the time reversible case of a general theorem of Bhattacharya is shown to imply the Kipnis-Varadhan functional central limit theorem for ergodic Markov processes. To this end, a few results from semigroup theory, including the resolvent identity, are incoporated in Bhattacharya's range condition for the inifinitesimal generator. |
| title | On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes |
| topic | Probability 60J25, 60F05, 60G44 (Primary) 47B02, 47B25, 47B93 (Secondary) |
| url | https://arxiv.org/abs/2505.01045 |