Mathematics – Probability
Scientific paper
2007-04-06
Mathematics
Probability
25 pages; to appear in the Annals of Applied Probability
Scientific paper
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the spacings between the Brownian motions arranged in increasing order. For finitely many Brownian motions interacting in this manner, we characterize drifts for which the family of laws of the vector of spacings is tight, and show its convergence to a unique stationary joint distribution given by independent exponential distributions with varying means. We also study one particular countably infinite system, where only the minimum Brownian particle gets a constant upward drift, and prove that independent and identically distributed exponential spacings remain stationary under the dynamics of such a process. Some related conjectures in this direction have also been discussed.
Pal Soumik
Pitman Jim
No associations
LandOfFree
One-dimensional Brownian particle systems with rank dependent drifts 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 One-dimensional Brownian particle systems with rank dependent drifts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and One-dimensional Brownian particle systems with rank dependent drifts will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-6843