  Diffusion limits provide a framework for the asymptotic analysis of
stochastic gradient descent (SGD) schemes used in machine learning. We consider
an alternative framework, the Riemannian Langevin equation (RLE), that
generalizes the classical paradigm of equilibration in R^n to a Riemannian
manifold (M^n, g). The most subtle part of this equation is the description of
Brownian motion on (M^n, g). Explicit formulas are presented for some
fundamental cones.
