  Consider a probability measure supported by a regular geodesic ball in a
manifold. For any p larger than or equal to 1 we define a stochastic algorithm
which converges almost surely to the p-mean of the measure. Assuming
furthermore that the functional to minimize is regular around the p-mean, we
prove that a natural renormalization of the inhomogeneous Markov chain
converges in law into an inhomogeneous diffusion process. We give an explicit
expression of this process, as well as its local characteristic.
