A central limit theorem for the stochastic cable equation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909738291167232 |
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| author | Nishino, Soma |
| author_facet | Nishino, Soma |
| contents | We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is established in the total variation distance with mild conditions. We also establish a functional central limit theorem with a technical assumption. Furthermore, we show that this assumption holds in a special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A central limit theorem for the stochastic cable equation Nishino, Soma Probability 60H15 (Primary) 60F05, 60H07 (Secondary) We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is established in the total variation distance with mild conditions. We also establish a functional central limit theorem with a technical assumption. Furthermore, we show that this assumption holds in a special case. |
| title | A central limit theorem for the stochastic cable equation |
| topic | Probability 60H15 (Primary) 60F05, 60H07 (Secondary) |
| url | https://arxiv.org/abs/2506.02755 |