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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/2405.08795 |
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| _version_ | 1866913350554746880 |
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| author | Hu, Kevin Ramanan, Kavita Salkeld, William |
| author_facet | Hu, Kevin Ramanan, Kavita Salkeld, William |
| contents | We consider collections of SDEs indexed by a graph. Each SDE is driven by an additive Gaussian noise and each drift term interacts with all other SDEs within the graph neighbourhood. We derive the fundamental martingale for a class of Gaussian processes and use this to prove a Girsanov type theorem. Further, we use this to construct a clique factorisation to prove that the law of the interacting SDEs forms a 2-Markov Random Field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The fundamental martingale with applications to Markov Random Fields Hu, Kevin Ramanan, Kavita Salkeld, William Probability We consider collections of SDEs indexed by a graph. Each SDE is driven by an additive Gaussian noise and each drift term interacts with all other SDEs within the graph neighbourhood. We derive the fundamental martingale for a class of Gaussian processes and use this to prove a Girsanov type theorem. Further, we use this to construct a clique factorisation to prove that the law of the interacting SDEs forms a 2-Markov Random Field. |
| title | The fundamental martingale with applications to Markov Random Fields |
| topic | Probability |
| url | https://arxiv.org/abs/2405.08795 |