On the Geometry of Diffusion Operators and Stochastic Flows
Edition: 1st edition
Publisher: Springer-Verlag Telos
Published: May 15, 2000
Language: eng
Format: Paperback
Number of pages: 118
ISBN-13: 9783540667087
Subjects: Differential & Riemannian geometry; Functional analysis; Probability & statistics; Stochastics; Markov Processes; Mathematics; Medical / Nursing; Science/Mathematics; General; Probability & Statistics - General; Mathematical Analysis; Diffusion processes; Flows (Differentiable dynamica; Flows (Differentiable dynamical systems); Linear Operators
Description: 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 geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.