A simple construction of the continuum parabolic Anderson model on R2

被引：52
|
作者：
Hairer, Martin [1 ]
Labbe, Cyril [1 ]
机构：
[1] Univ Warwick, Coventry CV4 7AL, W Midlands, England
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2015年 / 20卷
基金：
欧洲研究理事会;
关键词：
parabolic Anderson model; PDEs; weights; renormalisation; EQUATIONS;
D O I：
10.1214/ECP.v20-4038
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We propose a simple construction of the solution to the continuum parabolic Anderson model on 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 R-2.
引用
收藏
页码：1 / 11
页数：11
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