Barycenters of measures transported by stochastic flows

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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



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