Stochastic algorithms for computing means of probability measures
Probability
2011-06-28 v1
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.
Cite
@article{arxiv.1106.5106,
title = {Stochastic algorithms for computing means of probability measures},
author = {Marc Arnaudon and Clément Dombry and Anthony Phan and Le Yang},
journal= {arXiv preprint arXiv:1106.5106},
year = {2011}
}