Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry

DOI10.3934/jgm.2017015zbMath1367.53031arXiv1512.08544OpenAlexW2963448537MaRDI QIDQ2361270

Anne Marie Svane, Stefan Sommer

Publication date: 30 June 2017

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08544

zbMATH Keywords

stochastic processesholonomysub-Riemannian geometryprobability distributionsBrownian motionsstochastic developmentnon-linear data analysis

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Probability distributions: general theory (60E05) Sub-Riemannian geometry (53C17)

Related Items

Most probable paths for anisotropic Brownian motions on manifolds, Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018, Differential geometry and stochastic dynamics with deep learning numerics, An infinitesimal probabilistic model for principal component analysis of manifold valued data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• Sub-Riemannian geometry
• Minoration en temps petit de la densité d'une diffusion dégénérée. (Lower estimate for small times of the density of a degenerate diffusion)
• The Onsager-Machlup function for diffusion processes
• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• Any sub-Riemannian metric has points of smoothness
• Small-time heat kernel asymptotics at the sub-Riemannian cut locus
• Evolution Equations with Anisotropic Distributions and Diffusion PCA
• On the differential geometry of frame bundles of Riemannian manifolds.
• Probabilistic Principal Component Analysis
• Computational anatomy: an emerging discipline
• Orbits of Families of Vector Fields and Integrability of Distributions
• Diffusion processes in a small time interval