INVARIANT MEASURE SELECTION BY NOISE. AN EXAMPLE

被引：7
|
作者：
Mattingly, Jonathan C. [1 ,2 ]
Pardoux, Etienne [3 ]
机构：
[1] Duke Univ, Dept Math, Durham, NC 27708 USA
[2] Duke Univ, Dept Stat Sci, Durham, NC 27708 USA
[3] Univ Aix Marseille 1, Lab Anal, F-13453 Marseille 13, France
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 10期
基金：
美国国家科学基金会;
关键词：
Inviscid limits; zero noise limit; invariant measure selection; stochastic dynamically systems; DYNAMICAL-SYSTEMS; EQUATIONS; KDV;
D O I：
10.3934/dcds.2014.34.4223
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.
引用
收藏
页码：4223 / 4257
页数：35
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