Instantaneous blowup for interacting SDEs with superlinear drift
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918294175350784 |
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| author | Joseph, Mathew Ovhal, Shubham |
| author_facet | Joseph, Mathew Ovhal, Shubham |
| contents | We consider a system of interacting SDEs on the integer lattice with multiplicative noise and a drift satisfying the finite Osgood's condition. We show instantaneous everywhere blowup for initial profiles decaying slower than $\exp \left( -\sqrt{\big|\log |x|\big|}\right)$. We employ the splitting-up method to compare the interacting system to a one-dimensional SDE which blows up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instantaneous blowup for interacting SDEs with superlinear drift Joseph, Mathew Ovhal, Shubham Probability We consider a system of interacting SDEs on the integer lattice with multiplicative noise and a drift satisfying the finite Osgood's condition. We show instantaneous everywhere blowup for initial profiles decaying slower than $\exp \left( -\sqrt{\big|\log |x|\big|}\right)$. We employ the splitting-up method to compare the interacting system to a one-dimensional SDE which blows up. |
| title | Instantaneous blowup for interacting SDEs with superlinear drift |
| topic | Probability |
| url | https://arxiv.org/abs/2506.21164 |