Stochastic algorithms for computing means of probability pdf

Stochastic algorithms for computing means of probability

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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

• Creator/s: Marc Arnaudon, Clément Dombry, Anthony Phan, Le Yang
• Date: 6/25/2011

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