5
IRUS TotalDownloads
Altmetric
Barycenters of measures transported by stochastic flows
File | Description | Size | Format | |
---|---|---|---|---|
0507460v1.pdf | Accepted version | 398.15 kB | Adobe PDF | View/Open |
Title: | Barycenters of measures transported by stochastic flows |
Authors: | Arnaudon, M Li, X-M |
Item 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. |
Issue Date: | 1-Jul-2005 |
URI: | http://hdl.handle.net/10044/1/54084 |
DOI: | https://dx.doi.org/10.1214/009117905000000071 |
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 |
Keywords: | 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 |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences |