Integral identity and measure estimates for stationary Fokker-Planck equations
Integral identity and measure estimates for stationary Fokker-Planck equations
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DOI：
10.1214/14-aop917
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发表时间：
2014-01
期刊：
影响因子：
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通讯作者：
Wen Huang;Min Ji;Zhenxin Liu;Y. Yi
中科院分区：
文献类型：
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作者：
Wen Huang;Min Ji;Zhenxin Liu;Y. Yi
在${\mathbb{R}}^n$的一般定域上，考虑具有$L^p_{\ mathm {loc}}$漂移项和$W^{1,p}_{\ mathm {loc}}$扩散项的Fokker-Planck方程。通过导出一个积分恒等式，我们给出了关于扩散和类李雅普诺夫函数或反李雅普诺夫函数的外域正则平稳测度的几个测度估计。这些估计对于一般区域内平稳测度的存在性和不存在性以及扩散消失时平稳测度的集中和极限行为等问题都是有用的。
We consider a Fokker-Planck equation in a general domain in ${\mathbb{R}}^n$ with $L^p_{\mathrm{loc}}$ drift term and $W^{1,p}_{\mathrm{loc}}$ diffusion term for any $p>n$. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit behaviors of stationary measures as diffusion vanishes.