Mathematics – Probability
Scientific paper
2011-06-25
Mathematics
Probability
Scientific paper
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.
Arnaudon Marc
Dombry Clément
Phan Anthony
Yang Le
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