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Multiplicative stochastic heat equations on the whole space
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Hairer, Martin and Labbe, C. (2018) Multiplicative stochastic heat equations on the whole space. Journal of the European Mathematical Society, 20 (4). pp. 1005-1054. doi:10.4171/JEMS/781
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Official URL: http://doi.org/10.4171/JEMS/781
Abstract
We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are the parabolic Anderson model on R3, and the KPZ equation on R via the Cole–Hopf transform. To perform these constructions, we adapt the theory of regularity structures to the setting of weighted Besov spaces. One particular feature of our construction is that it allows one to start both equations from a Dirac mass at the initial time.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations -- Numerical solutions, Anderson model -- Mathematical models | ||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | ||||||
| Publisher: | European Mathematical Society Publishing House | ||||||
| ISSN: | 1435-9855 | ||||||
| Official Date: | 15 March 2018 | ||||||
| Dates: |
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| Volume: | 20 | ||||||
| Number: | 4 | ||||||
| Page Range: | pp. 1005-1054 | ||||||
| DOI: | 10.4171/JEMS/781 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | Leverhulme Trust (LT), European Research Council (ERC) | ||||||
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