重尾密度的一维Fokker-Planck方程和泛函不等式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-03-28 DOI:10.1007/s00032-022-00352-3

Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani

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引用次数: 1

摘要

我们提出并讨论了为社会经济问题建模的一维福克-普朗克方程趋向平衡的问题，以及具有多项式尾的概率密度的poincar、Wirtinger和对数Sobolev类型的一维泛函不等式(带权重)之间的联系。作为主要的例子，我们考虑在\(\mathbb R_+\)上取值的逆伽马密度和在\(\mathbb R\)上取值的柯西型密度所满足的不等式。

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One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities

We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities, taking values on \(\mathbb R_+\), and Cauchy-type densities, taking values on \(\mathbb R\).

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.