Multiplicative stochastic heat equations on the whole space
Abstract
We carry out the construction of some illposed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the ColeHopf 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.07162
 Bibcode:
 2015arXiv150407162H
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability
 EPrint:
 52 pages