Analytically weak solutions to stochastic heat equations with spatially rough noise
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916228317052928 |
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| author | Gerencsér, Máté |
| author_facet | Gerencsér, Máté |
| contents | In [HHL+17] the authors showed existence and uniqueness of solutions to the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and rougher than white in space (in particular, its covariance is not a measure). Here we present a simple alternative to derive such results by considering the equations in the analytically weak sense, using either the variational approach or Krylov's $L^p$-theory. Various improvements are obtained as corollaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytically weak solutions to stochastic heat equations with spatially rough noise Gerencsér, Máté Probability 60H15 In [HHL+17] the authors showed existence and uniqueness of solutions to the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and rougher than white in space (in particular, its covariance is not a measure). Here we present a simple alternative to derive such results by considering the equations in the analytically weak sense, using either the variational approach or Krylov's $L^p$-theory. Various improvements are obtained as corollaries. |
| title | Analytically weak solutions to stochastic heat equations with spatially rough noise |
| topic | Probability 60H15 |
| url | https://arxiv.org/abs/2404.18920 |