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

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].

### MSC:

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

### Keywords:

Riemannian manifold; martingale; connection; barycenters
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