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Multiplicative stochastic heat equations on the whole space

Hairer, Martin; Labbé, Cyril (2018), Multiplicative stochastic heat equations on the whole space, Journal of the European Mathematical Society, 20, 4, p. 1005-1054. 10.4171/JEMS/781

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Journal of the European Mathematical Society
Volume
20
Number
4
Publisher
European Mathematical Society
Pages
1005-1054
Publication identifier
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Author(s)
Hairer, Martin

Labbé, Cyril
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on R3, and on the other hand 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.
Subjects / Keywords
Stochastic partial differential equations; Numerical solutions; Anderson model; Mathematical models