Occupation Time Fluctuations in Branching Systems

D. A. Dawson (), L. G. Gorostiza () and A. Wakolbinger ()
Additional contact information
D. A. Dawson: The Fields Institute
L. G. Gorostiza: Centro de Investigación y de Estudios Avanzados
A. Wakolbinger: Johann Wolfgang Goethe–Universität

Journal of Theoretical Probability, 2001, vol. 14, issue 3, 729-796

Abstract: Abstract We consider particle systems in locally compact Abelian groups with particles moving according to a process with symmetric stationary independent increments and undergoing one and two levels of critical branching. We obtain long time fluctuation limits for the occupation time process of the one- and two-level systems. We give complete results for the case of finite variance branching, where the fluctuation limits are Gaussian random fields, and partial results for an example of infinite variance branching, where the fluctuation limits are stable random fields. The asymptotics of the occupation time fluctuations are determined by the Green potential operator G of the individual particle motion and its powers G 2,G 3, and by the growth as t→∞ of the operator $$G_t = \int_0^t {T_s } ds$$ and its powers, where T t is the semigroup of the motion. The results are illustrated with two examples of motions: the symmetric α-stable Lévy process in $$\mathbb{R}^d (0

Keywords: multilevel branching particle system; occupation time; fluctuation; Green potential; weak and strong transience; stable Lévy process; hierarchical random walk; critical dimensions (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1023/A:1017597107544 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:14:y:2001:i:3:d:10.1023_a:1017597107544

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1017597107544

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().