Research Catalog

Title

The geometry of filtering / K. David Elworthy, Yves LeJan, Xue-Mei Li.

Author

Elworthy, K. D.

Publication

Basel : Birkhäuser ; London : Springer [distributor], c2010.

Items in the Library & Off-site

Holdings

Details

Additional Authors

• Le Jan, Y. (Yves), 1952-
• Li, X-M. (Xue-Mei), 1964-

Description

xi, 169 p.; 24 cm.

Summary

• Filtering theory is the science of obtaining or estimating information about a system from partial and possibly flawed observations of it. The system itself may be random, and the flaws in the observations can be caused by additional noise. In this volume the randomness and noises will be of Gaussian white noise type so that the system can be modelled by a diffusion process; that is it evolves continuously in time in a Markovian way, the future evolution depending only on the present situation.
• The geometry which is the topic of this book is that determined by a map of one space N onto another, M, mapping a diffusion process, or operator, on N to one on M.
• This is the standard situation of systems governed by Ito type stochastic differential equations. The state space will be the smooth manifold, N, possibly infinite dimensional, and the "observations" will be obtained by a smooth map onto another manifold, N, say. We emphasise that the geometry is important even when both manifolds are Euclidean spaces. This can also be viewed from a purely partial differential equations viewpoint as one smooth second order elliptic partial differential operator lying above another, both with no zero order term.
• We consider the geometry of this situation with special emphasis on situations of geometric, stochastic analytic, or filtering interest. The most well studied case is one Brownian motion being mapped to another with a consequent skew product decomposition (or equivalently the case of Reimannian submersions). This sort of decomposition is generalised and a key to the rest of the book. It is used to study in particular, classical filtering, (semi- )connections determined by stochastic flows, and generalised Weitzenbock formulae. --Book Jacket.

Series Statement

Frontiers in mathematics

Uniform Title

Frontiers in mathematics.

Subject

• Distribution (Probability theory)
• Filters (Mathematics)
• Gaussian processes
• Global analysis (Mathematics)
• Global differential geometry
• Markov processes
• Mathematics

Bibliography (note)

• Includes bibliographical references (p. 159-166) and index.

Processing Action (note)

• committed to retain

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.

ISBN

• 9783034601757 (pbk.)
• 3034601751 (pbk.)

OCLC

449852844

Owning Institutions

Harvard Library