A diffusion process associated with Fréchet meansTools Le, Huiling (2015) A diffusion process associated with Fréchet means. Annals of Applied Probability, 25 (6). pp. 3033-3046. ISSN 1050-5164 Full text not available from this repository.
Official URL: http://projecteuclid.org/euclid.aoap/1443703768
AbstractThis paper studies rescaled images, under exp−1μ, of the sample Fréchet means of i.i.d. random variables {Xk|k≥1} with Fréchet mean μ on a Rie-mannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp−1μ(X1), this linear transformation also depends on the global Riemannian structure of the manifold
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