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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04169 |
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| _version_ | 1866911192373526528 |
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| author | Zhang, Shao-Qin |
| author_facet | Zhang, Shao-Qin |
| contents | Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a stationary distribution, and links the instability to a spectral property of the generator of the corresponding linearized semigroup to the stochastic equation. Concrete examples, such as the granular media equation with double-wells landscapes, are given to illustrate our main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on the instability of equilibria for distribution dependent SDEs Zhang, Shao-Qin Probability 60H10 Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a stationary distribution, and links the instability to a spectral property of the generator of the corresponding linearized semigroup to the stochastic equation. Concrete examples, such as the granular media equation with double-wells landscapes, are given to illustrate our main result. |
| title | A Note on the instability of equilibria for distribution dependent SDEs |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/2510.04169 |