Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian...
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the und...
A basic 1982 treatment of stochastic differential equations on manifolds and their solution flows and the properties of Brownian motion on Riemannian manifolds.
A basic 1982 treatment of stochastic differential equations on manifolds and their solution flows and the properties of Brownian motion on Riemannian ...
