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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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, Engineering and Medicine > 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:	Date Event 2015 Published 10 June 2015 Accepted
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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