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

页码：1 / 11

页数：11

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