U-statistics of Ornstein-Uhlenbeck branching particle system

Details U-statistics of Ornstein-Uhlenbeck branching particle system U-statistics of Ornstein-Uhlenbeck branching particle system

2011-11-19

arxiv.org/abs/1111.4560v2

Mathematics

Probability

References update. arXiv admin note: substantial text overlap with arXiv:1007.1719

Scientific paper

We consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is known to fulfil a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem has been addressed. It turns out that the normalization and 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 Orstein-Uhlenbeck process. In the present paper we extend those results to $U$-statistics of the system proving a law of large numbers and a central limit theorem.

Affiliated with

Also associated with

No associations

Rating

U-statistics of Ornstein-Uhlenbeck branching particle system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with U-statistics of Ornstein-Uhlenbeck branching particle system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and U-statistics of Ornstein-Uhlenbeck branching particle system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-514681