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A simple construction of the continuum parabolic Anderson model on R2
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Hairer, Martin and Labbé, Cyril (2015) A simple construction of the continuum parabolic Anderson model on R2. Electronic Communications in Probability, 20 . 43. doi:10.1214/ECP.v20-4038
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Official URL: http://dx.doi.org/10.1214/ECP.v20-4038
Abstract
We propose a simple construction of the solution to the continuum parabolic Anderson model on R2 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 R2.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Heat equation , Differential equations, Partial | ||||||
| Journal or Publication Title: | Electronic Communications in Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1083-589X | ||||||
| Official Date: | 2015 | ||||||
| Dates: |
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| Volume: | 20 | ||||||
| Article Number: | 43 | ||||||
| DOI: | 10.1214/ECP.v20-4038 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | European Research Council (ERC), Leverhulme Trust (LT) |
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