The Geometry of Filtering

• Main Authors: Elworthy, K. David (Author), Le Jan, Yves (Author), Li, Xue-Mei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2010.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Numerical analysis.; Differential geometry.; Probabilities.; Numerical Analysis.; Probability Theory and Stochastic Processes.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian str...

Table of Contents:

• Diffusion Operators
• Decomposition of Diffusion Operators
• Equivariant Diffusions on Principal Bundles
• Projectible Diffusion Processes and Markovian Filtering
• Filtering with non-Markovian Observations
• The Commutation Property
• Example: Riemannian Submersions and Symmetric Spaces
• Example: Stochastic Flows
• Appendices.