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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

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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:
DateEvent
15 March 2018Published
2 June 2016Accepted
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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