论文标题
fokker-Planck方程和重尾密度的一维功能不平等
Fokker-Planck equations and one-dimensional functional inequalities for heavy tailed densities
论文作者
论文摘要
我们研究了具有多项式尾巴的概率密度，研究了庞加莱，对数Sobolev和Wirewtinger类型的一维功能不平等。作为主要示例，我们获得了通过反伽马密度，$ r _+$的值和库奇型密度满足的尖锐不平等，并以$ r $ $ $ $ $ $ $ $ $ $ $ R $。在最后一个情况下，我们改善了Bobkov和Ledoux在2009年获得的结果，通过在对数Sobolev不平等中引入更好的权重功能。结果是通过诉诸于具有这些密度作为稳态的Fokker-Planck类型方程来获得的。
We study one-dimensional functional inequalities of the type of Poincaré, logarithmic Sobolev and Wirtinger, with weight, for probability densities with polynomial tails. As main examples, we obtain sharp inequalities satisfied by inverse Gamma densities, taking values on $R_+$, and Cauchy-type densities, taking values on $R$. In this last case, we improve the result obtained by Bobkov and Ledoux in 2009 by introducing a better weight function in the logarithmic Sobolev inequality. The results are obtained by resorting to Fokker-Planck type equations which possess these densities as steady states.
