By K.D. Elworthy;Y. Le Jan;Xue-Mei Li

Stochastic differential equations, and Hoermander shape representations of diffusion operators, can be sure a linear connection linked to the underlying (sub)-Riemannian constitution. this is often systematically defined, including its invariants, after which exploited to debate qualitative homes of stochastic flows, and research on direction areas of compact manifolds with diffusion measures. this could be priceless to stochastic analysts, particularly people with pursuits in stochastic flows, limitless dimensional research, or geometric research, and in addition to researchers in sub-Riemannian geometry. A simple heritage in differential geometry is thought, however the building of the connections is particularly direct and itself offers an intuitive and urban creation. wisdom of stochastic research can be assumed for later chapters.