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Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications
     

Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications

by Gregory S. Chirikjian
 

The subjects of shastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually,

Overview

The subjects of shastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of shastic, geometric, and group-theoretic concepts in the modeling of physical phenomena.

Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time shastic processes, differential geometry, and the probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including shastic geometry, geometric aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups.

Key features and topics of Volume 2:

* The author reviews the concept of—andfunctions and integration on—Lie groups with many concrete examples.

* Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied shastic processes on Lie groups or geometric aspects of probability and statistics.

*Specific application areas are explored, including biomolecular statistical mechanics and information-driven motion in robotics.

* The concrete presentation style makes it easy for readers to obtain numerical solutions for their own problems; the emphasis is on how to calculate quantities rather than how to prove theorems.

* Modern problems at the interface of mechanics, control theory, and communications are handled in a unified framework and multiple directions for future research are explored.

Shastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering.

Product Details

ISBN-13:
9780817649432
Publisher:
Birkhauser Verlag
Publication date:
11/15/2011
Series:
Applied and Numerical Harmonic Analysis Series
Edition description:
1st Edition.
Pages:
435
Product dimensions:
7.00(w) x 10.00(h) x 1.00(d)

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