Multiplicative stochastic heat equations on the whole space
Martin HairerUniversity of Warwick, Coventry, UK
Cyril LabbéUniversité Paris-Dauphine, France
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 , and the KPZ equation on 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.
Cite this article
Martin Hairer, Cyril Labbé, Multiplicative stochastic heat equations on the whole space. J. Eur. Math. Soc. 20 (2018), no. 4, pp. 1005–1054DOI 10.4171/JEMS/781