Geodesic
Multiplicative stochastic heat equations on the whole space
Journal of the European Mathematical Society, Tome 20 (2018) no. 4, pp. 1005-1054 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/781
Classification : 60-XX, 35-XX
Keywords: Stochastic heat equation, parabolic Anderson model, white noise, weighted spaces, regularity structures 
@article{JEMS_2018_20_4_a4,
     author = {Martin Hairer and Cyril Labb\'e},
     title = {Multiplicative stochastic heat equations on the whole space},
     journal = {Journal of the European Mathematical Society},
     pages = {1005--1054},
     year = {2018},
     volume = {20},
     number = {4},
     doi = {10.4171/jems/781},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/781/}
}
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Martin Hairer; Cyril Labbé. Multiplicative stochastic heat equations on the whole space. Journal of the European Mathematical Society, Tome 20 (2018) no. 4, pp. 1005-1054. doi: 10.4171/jems/781

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