Electronic Communications in Probability

A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$

Martin Hairer and Cyril Labbé

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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 $\mathbf{R}^2$.

Article information

Source
Electron. Commun. Probab. Volume 20 (2015), paper no. 43, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320970

Digital Object Identifier
doi:10.1214/ECP.v20-4038

Mathematical Reviews number (MathSciNet)
MR3358965

Zentralblatt MATH identifier
1332.60094

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
parabolic Anderson model PDEs weights renormalisation

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Hairer, Martin; Labbé, Cyril. A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$. Electron. Commun. Probab. 20 (2015), paper no. 43, 11 pp. doi:10.1214/ECP.v20-4038. https://projecteuclid.org/euclid.ecp/1465320970.


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