热力学条件下空间生灭过程局部统计的泛函中心极限定理

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-10-01 DOI:10.1214/22-aap1912

Efe Onaran, Omer Bobrowski, Robert J. Adler

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引用次数: 1

摘要

我们给出了在动态泊松过程上定义的局部泛函在过程水平上的正态逼近结果。我们在这里研究的动力学是马尔可夫生-死过程的动力学。我们在所谓的热力学条件下证明了泛函极限定理。我们的结果适用于随机几何文献中一些感兴趣的函数，包括随机几何图中的子图和分量计数。

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Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are those of a Markov birth–death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.

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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.