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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.04515 |
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| _version_ | 1866914833125867520 |
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| author | Adams, Zachary P. |
| author_facet | Adams, Zachary P. |
| contents | We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron map of reaction-diffusion equations and neural field equations. Using the regularity properties proven here, we are able to obtain a strong Itô formula for the isochronal phase of stochastically perturbed travelling waves, spiral waves, and other patterns appearing in SPDEs driven by white noise, even for SPDEs that only admit mild solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_04515 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Existence, Regularity, and a Strong Itô Formula for the Isochronal Phase of SPDE Adams, Zachary P. Probability We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron map of reaction-diffusion equations and neural field equations. Using the regularity properties proven here, we are able to obtain a strong Itô formula for the isochronal phase of stochastically perturbed travelling waves, spiral waves, and other patterns appearing in SPDEs driven by white noise, even for SPDEs that only admit mild solutions. |
| title | Existence, Regularity, and a Strong Itô Formula for the Isochronal Phase of SPDE |
| topic | Probability |
| url | https://arxiv.org/abs/2109.04515 |