Disagreement coupling of Gibbs processes with an application to Poisson approximation

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-10-01 DOI:10.1214/22-aap1916

Moritz Otto

引用次数: 6

Abstract

We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach of Hofer-Temmel (Electron. J. Probab. 24 (2019) 1–22) and Hofer-Temmel and Houdebert (Stochastic Process. Appl. 129 (2019) 3922–3940) we will use this to couple two finite Gibbs processes with different boundary conditions. As one application we will establish Poisson approximation of point processes derived from certain infinite volume Gibbs processes via dependent thinning. As another application we shall discuss empty space probabilities of certain Gibbs processes.

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吉布斯过程的不一致耦合及其在泊松近似中的应用

讨论了构造给定Papangelou强度的有限Gibbs过程的一种细化和嵌入方法。扩展Hofer-Temmel(电子)方法。[j] .数理学报，24(2019):1-22。应用程序129(2019)3922-3940)，我们将使用它来耦合两个具有不同边界条件的有限吉布斯过程。作为一个应用，我们将通过相关减薄建立由某些无限体积吉布斯过程导出的点过程的泊松近似。作为另一个应用，我们将讨论某些吉布斯过程的空空间概率。

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

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.