On a class of Fokker–Planck equations with subcritical confinement

IF 0.6 4区 数学 Q3 MATHEMATICS
G. Toscani, M. Zanella
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引用次数: 3

Abstract

We study the relaxation to equilibrium for a class linear onedimensional Fokker–Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker–Planck equations is that, for any given probability density e(x), the diffusion coefficient can be built to have e(x) as steady state. This representation of the equilibrium density can be fruitfully used to obtain one-dimensional Wirtinger-type inequalities and to recover, for a sufficiently regular density e(x), a polynomial rate of convergence to equilibrium. Numerical results then confirm the theoretical analysis, and allow to conjecture that convergence to equilibrium with positive rate still holds for steady states characterized by a very slow polynomial decay at infinity.
关于一类亚临界约束的Fokker-Planck方程
我们研究了一类线性一维Fokker–Planck方程的弛豫到平衡,该方程具有特定的亚临界约束势。这类Fokker–Planck方程的一个有趣的特征是,对于任何给定的概率密度e(x),扩散系数都可以建立为以e(x)为稳态。平衡密度的这种表示可以有效地用于获得一维Wirtinger型不等式,并且对于足够规则的密度e(x),可以恢复到平衡的多项式收敛率。然后,数值结果证实了理论分析,并允许推测,对于以无穷远处非常缓慢的多项式衰减为特征的稳态,收敛到正速率平衡仍然成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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