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2010 Particle systems with quasi-homogeneous initial states and their occupation time fluctuations
Tomasz Bojdecki, Luis Gorostiza, Anna Talarczyk
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Electron. Commun. Probab. 15: 191-202 (2010). DOI: 10.1214/ECP.v15-1547


We consider particle systems in $R$ with initial configurations belonging to a class of measures that obey a quasi-homogeneity property, which includes as special cases homogeneous Poisson measures and many deterministic measures (simple example: one atom at each point of $Z$). The particles move independently according to an alpha-stable Levy process, $\alpha > 1$, and we also consider the model where they undergo critical branching. Occupation time fluctuation limits of such systems have been studied in the Poisson case. For the branching system in ``low'' dimension the limit was characterized by a process called sub-fractional Brownian motion, and this process was attributed to the branching because it had appeared only in that case. In the present more general framework sub-fractional Brownian motion is more prevalent, namely, it also appears as a component of the limit for the system without branching in ``low'' dimension. A new method of proof, based on the central limit theorem, is used.


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Tomasz Bojdecki. Luis Gorostiza. Anna Talarczyk. "Particle systems with quasi-homogeneous initial states and their occupation time fluctuations." Electron. Commun. Probab. 15 191 - 202, 2010.


Accepted: 8 June 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60048
MathSciNet: MR2653724
Digital Object Identifier: 10.1214/ECP.v15-1547

Primary: 60F17
Secondary: 60G18 , 60G52 , 60J80

Keywords: branching , distribution-valued process , limit theorem , occupation time fluctuation , Particle system , Stable process , sub-fractional Brownian motion

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