Barycenters of measures transported by stochastic flows

DOI10.1214/009117905000000071zbMath1077.60039arXivmath/0507460OpenAlexW3099551650MaRDI QIDQ2569227

Marc Arnaudon, Xue-Mei Li

Publication date: 18 October 2005

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507460

zbMATH Keywords

manifoldBrownian motionconvex gemetry

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Strong limit theorems (60F15) Brownian motion (60J65) Martingales with continuous parameter (60G44) Random measures (60G57)

Related Items (6)

Bi-Invariant Dissimilarity Measures for Sample Distributions in Lie Groups ⋮ Stochastic algorithms for computing means of probability measures ⋮ NATURAL "FLOW" NOT IN LE JAN–RAIMOND FRAMEWORK ⋮ Medians and means in Finsler geometry ⋮ Discrete-time gradient flows and law of large numbers in Alexandrov spaces ⋮ A geometric path from zero Lyapunov exponents to rotation cocycles

Cites Work

• Manifolds of nonpositive curvature
• Geometry of horospheres
• Martingales on Riemannian manifolds with prescribed limit
• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• Differentiable and analytic families of continuous martingales in manifolds with connection
• Linear bounds for stochastic dispersion.
• Central limit theorem in negative curvature
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• Visibility manifolds
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Convex geometry and nonconfluent γ-martingales II: well-posedness and γ-martingale convergence
• Convexity and the Hemisphere
• The Propeller: A Counterexample to a Conjectured Criterion for the Existence of Certain Convex Functions
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