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| Main Author: | |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1803.01744 |
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| _version_ | 1866910362755923968 |
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| author | Bellingeri, Carlo |
| author_facet | Bellingeri, Carlo |
| contents | We use the theory of regularity structures to develop an Itô formula for $u$, the solution of the one dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular for any smooth enough function $φ$ we can express the random distribution $(\partial_t-\partial_{xx})φ(u)$ and the random field $φ(u)$ in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of stochastic calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_01744 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An Itô type formula for the additive stochastic heat equation Bellingeri, Carlo Probability 60H15 We use the theory of regularity structures to develop an Itô formula for $u$, the solution of the one dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular for any smooth enough function $φ$ we can express the random distribution $(\partial_t-\partial_{xx})φ(u)$ and the random field $φ(u)$ in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of stochastic calculus. |
| title | An Itô type formula for the additive stochastic heat equation |
| topic | Probability 60H15 |
| url | https://arxiv.org/abs/1803.01744 |