Open Access
Translator Disclaimer
2015 A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$
Martin Hairer, Cyril Labbé
Author Affiliations +
Electron. Commun. Probab. 20: 1-11 (2015). DOI: 10.1214/ECP.v20-4038

Abstract

We propose a simple construction of the solution to the continuum parabolic Anderson model on $\mathbf{R}^2$ which does not rely on any elaborate arguments and makes extensive use of the linearity of the equation. A logarithmic renormalisation is required to counterbalance the divergent product appearing in the equation. Furthermore, we use time-dependent weights in our spaces of distributions in order to construct the solution on the unbounded space $\mathbf{R}^2$.

Citation

Download Citation

Martin Hairer. Cyril Labbé. "A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$." Electron. Commun. Probab. 20 1 - 11, 2015. https://doi.org/10.1214/ECP.v20-4038

Information

Accepted: 10 June 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1332.60094
MathSciNet: MR3358965
Digital Object Identifier: 10.1214/ECP.v20-4038

Subjects:
Primary: 60H15

JOURNAL ARTICLE
11 PAGES


SHARE
Back to Top