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Journal Articles Stochastic Processes and their Applications Year : 2012

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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Dates and versions

hal-00540623 , version 1 (28-11-2010)
hal-00540623 , version 2 (24-06-2011)

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Cite

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