@article{ECP1547,
author = {Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk},
title = {Particle systems with quasi-homogeneous initial states and their occupation time fluctuations},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {particle system; branching; occupation time fluctuation; limit theorem; stable process; distribution-valued process; sub-fractional Brownian motion},
abstract = {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.},
pages = {no. 18, 191-202},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1547},
url = {http://ecp.ejpecp.org/article/view/1547}}