Expansion and attraction of RDS: long time behavior of the solution to singular SDE
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917651861733376 |
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| author | Ling, Chengcheng Scheutzow, Michael |
| author_facet | Ling, Chengcheng Scheutzow, Michael |
| contents | We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the SDE can be split into two terms, one of which is singular and the radial component of the other term has a radial component of sufficient strength in the direction of the origin, then the random dynamical system generated by the SDE admits a pullback attractor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14202 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Expansion and attraction of RDS: long time behavior of the solution to singular SDE Ling, Chengcheng Scheutzow, Michael Probability Dynamical Systems 60H10, 60G17, 60J60, 60H50 We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the SDE can be split into two terms, one of which is singular and the radial component of the other term has a radial component of sufficient strength in the direction of the origin, then the random dynamical system generated by the SDE admits a pullback attractor. |
| title | Expansion and attraction of RDS: long time behavior of the solution to singular SDE |
| topic | Probability Dynamical Systems 60H10, 60G17, 60J60, 60H50 |
| url | https://arxiv.org/abs/2211.14202 |