$$U$$ U -Statistics of Ornstein–Uhlenbeck Branching Particle System

Radosław Adamczak () and Piotr Miłoś ()
Additional contact information
Radosław Adamczak: University of Warsaw
Piotr Miłoś: University of Warsaw

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1071-1111

Abstract: Abstract We consider a branching particle system consisting of particles moving according to the Ornstein–Uhlenbeck process in $$\mathbb {R}^d$$ R d and undergoing a binary, supercritical branching with a constant rate $$\lambda >0$$ λ > 0 . This system is known to fulfill a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem (CLT) has been addressed. It turns out that the normalization and the form of the limit in the CLT fall into three qualitatively different regimes, depending on the relation between the branching intensity and the parameters of the Ornstein–Uhlenbeck process. In the present paper, we extend those results to $$U$$ U -statistics of the system, proving a law of large numbers and CLT.

Keywords: Supercritical branching particle systems; $$U$$ U -statistics; Central limit theorem; Primary 60F05; 60J80; Secondary 60G20 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-013-0503-2 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:27:y:2014:i:4:d:10.1007_s10959-013-0503-2

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

DOI: 10.1007/s10959-013-0503-2

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 ().