On the Geometry of Diffusion Operators and Stochastic Flows

• Main Authors: Elworthy, K.D (Author, http://id.loc.gov/vocabulary/relators/aut), Le Jan, Y. (http://id.loc.gov/vocabulary/relators/aut), Li, Xue-Mei (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1720
• Subjects: Probabilities.; Functional analysis.; Differential geometry.; Global analysis (Mathematics).; Manifolds (Mathematics).; Probability Theory and Stochastic Processes.; Functional Analysis.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

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 properti...

Table of Contents:

• 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.