Convex barycenters and approximations of continuous martingales in manifolds. (Barycentres convexes et approximations des martingales continues dans les variétés.) (French) Zbl 0837.58037

Arnaudon, Marc

Azéma, J. (ed.) et al., Séminaire de probabilités XXIX. Berlin: Springer-Verlag. Lect. Notes Math. 1613, 70-85 (1995).

The author considers a small compact subset \(V\) of a manifold equipped with a linear connection. He gives a moment estimate for the diameter of the set of convex barycenters of probability measures supported by \(V\). This estimate is used for proving an approximation theorem for \(V\)-valued martingales.
For the entire collection see [Zbl 0826.00027].

Reviewer: V.A.Kaimanovich (Rennes)

MSC:

58J65	Diffusion processes and stochastic analysis on manifolds
60G44	Martingales with continuous parameter

Keywords:

Riemannian manifold; martingale; connection; barycenters