  A stochastic algorithm is proposed, finding the set of generalized means
associated to a probability measure on a compact Riemannian manifold M and a
continuous cost function on the product of M by itself. Generalized means
include p-means for p>0, computed with any continuous distance function, not
necessarily the Riemannian distance. They also include means for lengths
computed from Finsler metrics, or for divergences. The algorithm is fed
sequentially with independent random variables Y_n distributed according to the
probability measure on the manifold and this is the only knowledge of this
measure required. It evolves like a Brownian motion between the times it jumps
in direction of the Y_n. Its principle is based on simulated annealing and
homogenization, so that temperature and approximations schemes must be tuned
up. The proof relies on the investigation of the evolution of a
time-inhomogeneous L^2 functional and on the corresponding spectral gap
estimates due to Holley, Kusuoka and Stroock.
