Stochastic algorithms for computing means of probability measures

Marc Arnaudon, Clément Dombry, Anthony Phan and Le Yang

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1437-1455

Abstract: Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any p≥1 we define a stochastic algorithm which converges almost surely to the p-mean ep of μ. Assuming furthermore that the functional to minimize is regular around ep, 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.

Keywords: Mean; Barycenter; Probability measure; Riemannian geometry; Convexity; Geodesic ball; Markov chain; Convergence in law; Invariance principle (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2011.12.011

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