Overview
- Unique work: the only book to use tools and concepts from several mathematical areas usually treated in separate books—stochastic processes, information theory, and Lie theory—thereby building bridges between topics rarely studied by the same individuals
- Extensive exercises and numerous examples used to motivate concepts with an emphasis on modeling physical phenomena
- Concrete presentation makes it easy for readers to obtain numerical solutions for their own problems
- Applications to a variety of areas, including conformational fluctuations of DNA, infotaxis, statistical mechanics, and biomolecular information theory
- Suitable as a textbook for advanced undergraduate and graduate courses in applied stochastic processes or differential geometry
- For a broad audience of advanced undergraduate and graduate students, researchers, and practitioners in applied mathematics, the physical sciences, and engineering
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
- Gaussian distributions, heat equation
- Lie groups
- Shannon's information theory
- biomolecular information theory
- coding problems on Lie groups
- conformational fluctuations of DNA
- differentiable manifolds
- differential forms
- diffusion processes, motion groups
- geometric robotic manipulator
- information theory and group theory
- infotaxis
- rotational Brownian motion
- statistical mechanics, ergodic theory
- stochastic processes on Lie groups
About this book
The subjects of stochastic 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 stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena.
Volume 2 builds on the fundamentals presented in Volume 1, delving deeper into relationships among stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Stochastic 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.
Authors and Affiliations
Bibliographic Information
Book Title: Stochastic Models, Information Theory, and Lie Groups, Volume 2
Book Subtitle: Analytic Methods and Modern Applications
Authors: Gregory S. Chirikjian
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-0-8176-4944-9
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-0-8176-4943-2Published: 15 November 2011
eBook ISBN: 978-0-8176-4944-9Published: 16 November 2011
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XXVII, 435
Topics: Applications of Mathematics, Mathematical and Computational Engineering, Differential Geometry, Probability Theory and Stochastic Processes, Topological Groups, Lie Groups, Mathematical Methods in Physics