%0 Journal Article %1 Bojdecki20061 %A Bojdecki, T. %A Gorostiza, L.G. %A Talarczyk, A. %D 2006 %J Stochastic Processes and their Applications %K Gaussian_processes limit_theorems particle_systems branching_processes %N 1 %P 1 - 18 %R 10.1016/j.spa.2005.07.002 %T Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence %U http://www.sciencedirect.com/science/article/pii/S0304414905001043 %V 116 %X We give a functional limit theorem for the fluctuations of the rescaled occupation time process of a critical branching particle system in R d with symmetric $\alpha$-stable motion and $< d < 2 \alpha$, which leads to a long-range dependence process involving sub-fractional Brownian motion. We also give an analogous result for the system without branching and $d < \alpha$ , which involves fractional Brownian motion. We use a space–time random field approach.

@article{Bojdecki20061, abstract = {We give a functional limit theorem for the fluctuations of the rescaled occupation time process of a critical branching particle system in R d with symmetric $\alpha$-stable motion and $\alpha < d < 2 \alpha$, which leads to a long-range dependence process involving sub-fractional Brownian motion. We also give an analogous result for the system without branching and $d < \alpha$ , which involves fractional Brownian motion. We use a space–time random field approach.}, added-at = {2012-08-31T03:37:44.000+0200}, author = {Bojdecki, T. and Gorostiza, L.G. and Talarczyk, A.}, biburl = {https://www.bibsonomy.org/bibtex/20f4786db405d09ed5e112d5f6f4e8cfe/peter.ralph}, doi = {10.1016/j.spa.2005.07.002}, interhash = {a2129b34fb0186591007f605e720ccaa}, intrahash = {0f4786db405d09ed5e112d5f6f4e8cfe}, issn = {0304-4149}, journal = {Stochastic Processes and their Applications}, keywords = {Gaussian_processes limit_theorems particle_systems branching_processes}, number = 1, pages = {1 - 18}, timestamp = {2013-03-01T22:31:59.000+0100}, title = {Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence}, url = {http://www.sciencedirect.com/science/article/pii/S0304414905001043}, volume = 116, year = 2006 }