Occupation times of subcritical branching immigration systems with Markov motion, CLT and deviation principles
type: Item
instance of: scholarly article
zbMATH Open document ID: 1253.60048
DOI: 10.1142/S0219025712500026
author: Piotr Miłoś
published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics
publication date: 2012-06-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.0777
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 60J68
zbMATH DE Number: 6044890
zbMATH Keywords: functional limit theorems
zbMATH Keywords: occupation time fluctuations
zbMATH Keywords: branching particle systems
zbMATH Keywords: superprocesses
zbMATH Keywords: subcritical branching with immigration
zbMATH Keywords: central limit theorem (CLT)
MaRDI profile type: Publication
arXiv ID: 0911.0777
cites work: A functional CLT for the occupation time of a state-dependent branching random walk
cites work: Limit theorems for occupation time fluctuations of branching systems. II: Critical and large dimensions
cites work: Occupation time fluctuations of an infinite-variance branching system in large dimensions
cites work: Large deviations for the occupation time functional of a Poisson system of independent Brownian particles
cites work: LARGE AND MODERATE DEVIATIONS FOR OCCUPATION TIMES OF IMMIGRATION SUPERPROCESSES
cites work: Large deviations for the three-dimensional super-Brownian motion
cites work: A LARGE DEVIATION FOR OCCUPATION TIME OF SUPER α-STABLE PROCESS
cites work: Limit theorems on large deviations for semimartingales
cites work: Occupation times of subcritical branching immigration systems with Markov motions
cites work: OCCUPATION TIME FLUCTUATION LIMITS OF INFINITE VARIANCE EQUILIBRIUM BRANCHING SYSTEMS
cites work: Moderate deviations and functional LIL for super-Brownian motion
OpenAlex ID: W3101388169
title: Occupation times of subcritical branching immigration systems with Markov motion, CLT and deviation principles
review text: The author studies two closely related stochastic models. The first is a subcritical branching particle system with immigration. The particles move independently in \(\mathbb{R}^d\) according to a time-homogeneous Markov family. The lifetime of each particle is exponential; when a particle dies it has either two offspring particles with probability \(q\) or none with probability \(1-q\), where \(q < 1/2\). New particles immigrate according to a homogeneous Poisson random field in time and space.NEWLINENEWLINEThe second model is a limiting case of the first, a measure-valued time-homogeneous Markov process, that is, a superprocess. Let \((N_t)_{t \geq 0}\) denote either of these two processes; the main objective of the paper is to study the rescaled occupation time process NEWLINE\[NEWLINE Y_T(t) := \frac{1}{F_T} \int_0^{Tt} N_s\, ds, \quad t \geq 0, NEWLINE\]NEWLINE and its fluctuation NEWLINE\[NEWLINE X_T(t) := \frac{1}{F_T} \int_0^{Tt} (N_s - \operatorname{E}N_s)\, ds, \quad t \geq 0, NEWLINE\]NEWLINE where \(F_T\) denotes a suitable deterministic norming which may vary from case to case.NEWLINENEWLINEUnder certain assumptions, the paper gives functional central limit theorems, large and moderate deviation theorems for the processes \(X_T\) and \(Y_T\), with both models. A more detailed version of the paper can be found in the extended version [\url{arXiv:0911.0777}].
reviewed by: Tamas Szabados
description: scientific article; zbMATH DE number 6044890