Stochastic algorithms for computing means of probability measures

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Arnaudon, Marc¹  Dombry, Clement¹  Phan, Anthony¹  Yang, Le¹ 

[1] Univ Poitiers, Lab Math & Applicat, CNRS, UMR 6086, F-86962 Futuroscope, France

关键词: Mean;    Barycenter;    Probability measure;    Riemannian geometry;    Convexity;    Geodesic ball;    Markov chain;    Convergence in law;    Invariance principle;   

DOI  :  10.1016/j.spa.2011.12.011

来源: Elsevier

【 摘 要 】

Consider a probability measure mu 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 e(p) of mu. Assuming furthermore that the functional to minimize is regular around e(p), 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. (c) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free