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Stochastic algorithms for computing means of probability measures

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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https://hal.archives-ouvertes.fr/hal-00540623
Contributor : Marc Arnaudon Connect in order to contact the contributor
Submitted on : Friday, June 24, 2011 - 10:15:22 PM
Last modification on : Wednesday, October 20, 2021 - 3:21:46 AM
Long-term archiving on: : Sunday, December 4, 2016 - 7:41:21 PM

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Marc Arnaudon, Clément Dombry, Anthony Phan, Le Yang. Stochastic algorithms for computing means of probability measures. Stochastic Processes and their Applications, Elsevier, 2012, 122, pp.1437-1455. ⟨10.1016/j.spa.2011.12.011⟩. ⟨hal-00540623v2⟩

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