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arXiv · 1106.5106

Stochastic algorithms for computing means of probability measures

Marc Arnaudon·Clément Dombry·Anthony Phan·Le Yang
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Abstract

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.

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Marc Arnaudon, Clément Dombry, Anthony Phan, Le Yang. 2011-06-25. Stochastic algorithms for computing means of probability measures. https://arxiv.org/abs/1106.5106

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