FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LOCAL STATISTICS OF SPATIAL BIRTH–DEATH PROCESSES IN THE THERMODYNAMIC REGIME

Efe Onaran; Omer Bobrowski; Robert J. Adler

doi:10.1214/22-AAP1912

FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LOCAL STATISTICS OF SPATIAL BIRTH–DEATH PROCESSES IN THE THERMODYNAMIC REGIME

Efe Onaran, Omer Bobrowski, Robert J. Adler

Research output: Contribution to journal › Article › peer-review

Abstract

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in R^d. 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.

Original language	English
Pages (from-to)	3958-3986
Number of pages	29
Journal	Annals of Applied Probability
Volume	33
Issue number	5
DOIs	https://doi.org/10.1214/22-AAP1912
State	Published - 2023

Keywords

functional central limit theorems
Ornstein–Uhlenbeck process
random geometric graphs
Spatial birth–death process

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/22-AAP1912

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abstract = "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.",

keywords = "functional central limit theorems, Ornstein–Uhlenbeck process, random geometric graphs, Spatial birth–death process",

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AU - Adler, Robert J.

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2023.

PY - 2023

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AB - 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.

KW - functional central limit theorems

KW - Ornstein–Uhlenbeck process

KW - random geometric graphs

KW - Spatial birth–death process

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JO - Annals of Applied Probability

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ER -

FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LOCAL STATISTICS OF SPATIAL BIRTH–DEATH PROCESSES IN THE THERMODYNAMIC REGIME

Abstract

Keywords

ASJC Scopus subject areas

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