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In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds.
A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
Charles Stein · 1972
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Large deviations and the Malliavin calculus
Jean-Michel Bismut · 1984
Earlier work this paper cites.
A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
Bruce K. Driver · 1992
Earlier work this paper cites.
Formulae for the derivatives of heat semigroups
K. David Elworthy and Xue-Mei Li · 1994
Earlier work this paper cites.
On the differentiation of heat semigroups and Poisson integrals
Anton Thalmaier · 1997
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Heat equation derivative formulas for vector bundles
Bruce K. Driver and Anton Thalmaier · 2001
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A Bismut type formula for the Hessian of heat semigroups
Marc Arnaudon, Holger Plank, and Anton Thalmaier · 2003
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Characterization of Brownian motion on manifolds through integration by parts
Elton P. Hsu · 2005
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Smooth approximation of Lipschitz functions on Riemannian manifolds
D. Azagra, J. Ferrera, F. López-Mesas, and Y. Rangel · 2007
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A short survey of Stein’s method
Sourav Chatterjee · 2014
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Analysis for diffusion processes on Riemannian manifolds
Feng-Yu Wang · 2014
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Geometric deep learning: going beyond euclidean data
M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst · 2017
Correction to: Multivariate approximations in Wasserstein distance by Stein’s method and Bismut’s formula
Xiao Fang, Qi-Man Shao, and Lihu Xu · 2019
Later among the works it cites.
Multivariate approximations in Wasserstein distance by Stein’s method and Bismut’s formula
Xiao Fang, Qi-Man Shao, and Lihu Xu · 2019
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Derivatives of Feynman-Kac semigroups
James Thompson · 2019
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Identifying constant curvature manifolds, Einstein manifolds, and Ricci parallel manifolds
Feng-Yu Wang · 2019
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Exponential contraction in Wasserstein distance on static and evolving manifolds
Li-Juan Cheng, Anton Thalmaier, and Shao-Qin Zhang · 2020
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Cited alongside, same era.