Barycenters of measures transported by stochastic flows
File(s)
Accepted version
Author(s)
Arnaudon, M
Li, X-M
Type
Journal Article
Abstract
We investigate the evolution of barycenters of masses transported by stochastic flows. The state spaces under consideration are smooth affine manifolds with certain convexity structure. Under suitable conditions on the flow and on the initial measure, the barycenter {Zt} is shown to be a semimartingale and is described by a stochastic differential equation. For the hyperbolic space the barycenter of two independent Brownian particles is a martingale and its conditional law converges to that of a Brownian motion on the limiting geodesic. On the other hand for a large family of discrete measures on suitable Cartan–Hadamard manifolds, the barycenter of the measure carried by an unstable Brownian flow converges to the Busemann barycenter of the limiting measure.
Date Issued
2005
Date Acceptance
2005-01-01
Citation
The Annals of Probability, 2005, 33, pp.1509-1543
ISSN
0091-1798
Start Page
1509
End Page
1543
Journal / Book Title
The Annals of Probability
Volume
33
Copyright Statement
© Institute of Mathematical Statistics, 2005
Identifier
http://dx.doi.org/10.1214/009117905000000071
Subjects
math.PR
60G60 (Primary) 60G57, 60H10, 60J65, 60G44, 60F05, 60F15 (Secondary)
0104 Statistics
Statistics & Probability
Notes
mrclass: 60G60 (58J65 60F05 60F15 60G44 60G57 60H10 60J65) mrnumber: 2150197 mrreviewer: Anna Karczewska
Article Number
4