
On the Geometry of Diffusion Operators and Stochastic Flows
Springer (Publisher)
Published on 17. November 1999
Book
Paperback/Softback
V, 105 pages
978-3-540-66708-7 (ISBN)
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.
More details
Series
Edition
1999 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
V, 105 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
454 gr
ISBN-13
978-3-540-66708-7 (9783540667087)
DOI
10.1007/BFb0103064
Schweitzer Classification
Content
Construction of connections.- The infinitesimal generators and associated operators.- Decomposition of noise and filtering.- Application: Analysis on spaces of paths.- Stability of stochastic dynamical systems.- Appendices.