Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527273 | Stochastic Processes and their Applications | 2012 | 19 Pages |
Abstract
Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any pâ¥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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marc Arnaudon, Clément Dombry, Anthony Phan, Le Yang,