Ergodicity for stochastic neural field equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909617061101568 |
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| author | Otsetova, Anna-Mariya Tölle, Jonas M. |
| author_facet | Otsetova, Anna-Mariya Tölle, Jonas M. |
| contents | We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by restricting the solution flow to an invariant subspace with a nonlocal metric. Under the assumption of a sufficiently large decay parameter relative to the noise intensity, the growth of the connectivity kernel, and the Lipschitz regularity of the activation function, we establish exponential ergodicity and exponential mixing of the associated Markovian Feller semigroup and the uniqueness of the invariant measure with second moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity for stochastic neural field equations Otsetova, Anna-Mariya Tölle, Jonas M. Probability Analysis of PDEs Dynamical Systems Functional Analysis 35K58, 35R60, 37A25, 37L40, 45K05, 47D07, 60H20, 92B20 We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by restricting the solution flow to an invariant subspace with a nonlocal metric. Under the assumption of a sufficiently large decay parameter relative to the noise intensity, the growth of the connectivity kernel, and the Lipschitz regularity of the activation function, we establish exponential ergodicity and exponential mixing of the associated Markovian Feller semigroup and the uniqueness of the invariant measure with second moments. |
| title | Ergodicity for stochastic neural field equations |
| topic | Probability Analysis of PDEs Dynamical Systems Functional Analysis 35K58, 35R60, 37A25, 37L40, 45K05, 47D07, 60H20, 92B20 |
| url | https://arxiv.org/abs/2505.14012 |