Lipschitzian norms and functional inequalities for birth-death processes

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series B Pub Date : 2023-01-01 DOI:10.3934/dcdsb.2023177

Wei Liu

引用次数: 0

Abstract

In this paper, we consider a birth-death process with generator $ \mathcal{L} $ and reversible invariant probability measure $ \pi. $ We identify explicitly the Lipschitzian norm of the solution of the Poisson equation $ -\mathcal{L} G = g-\pi(g) $ for $ |g|\le\varphi $. This leads to some transportation-information inequalities, concentration inequalities and Cheeger-type isoperimetric inequalities. Several examples are provided to illustrate the results.

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出生-死亡过程的Lipschitzian范数和功能不等式

本文考虑了一个具有生成器$ \mathcal{L} $和可逆不变概率测度$ \pi. $的生-死过程。我们明确地确定了$ |g|\le\varphi $的泊松方程$ -\mathcal{L} G = g-\pi(g) $解的Lipschitzian范数。这导致了一些运输信息不平等、浓度不平等和cheeger型等周不等式。提供了几个例子来说明结果。

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

Discrete and Continuous Dynamical Systems-Series B 数学-应用数学

CiteScore

2.80

自引率

8.30%

发文量

216

审稿时长

6 months

期刊介绍： Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.