Stochastic Models, Information Theory, and Lie Groups, Volume 2

Analytic Methods and Modern Applications

  • Gregory S. Chirikjian

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Gregory S. Chirikjian
    Pages 1-54
  3. Gregory S. Chirikjian
    Pages 55-78
  4. Gregory S. Chirikjian
    Pages 129-154
  5. Gregory S. Chirikjian
    Pages 155-185
  6. Gregory S. Chirikjian
    Pages 187-228
  7. Gregory S. Chirikjian
    Pages 271-312
  8. Gregory S. Chirikjian
    Pages 313-336
  9. Gregory S. Chirikjian
    Pages 337-359
  10. Gregory S. Chirikjian
    Pages 361-388
  11. Gregory S. Chirikjian
    Pages 411-418
  12. Back Matter
    Pages 419-433

About this book

Introduction

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 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, and the probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic 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—and functions 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 stochastic 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.

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.

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

Authors and affiliations

  • Gregory S. Chirikjian
    • 1
  1. 1.Department of Mechanical EngineeringThe Johns Hopkins UniversityBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4944-9
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4943-2
  • Online ISBN 978-0-8176-4944-9
  • About this book