Applied and Numerical Harmonic Analysis

Stochastic Models, Information Theory, and Lie Groups, Volume 1

Classical Results and Geometric Methods

Authors: Chirikjian, Gregory S.

  • 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
  • Concrete presentation makes it easy for readers to obtain numerical solutions for their own problems
  • Numerous examples used to motivate concepts with an emphasis on modeling physical phenomena
  • 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
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Buy this book

eBook $19.99
$54.99 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-0-8176-4803-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $29.99
$69.99 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-0-8176-4802-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 1:

* The author reviews stochastic processes and basic differential geometry in an accessible way for applied mathematicians, scientists, and engineers.

* Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

* The concept of Lie groups as continuous sets of symmetry operations is introduced.

* The Fokker–Planck Equation for diffusion processes in Euclidean space and on differentiable manifolds is derived in a way that can be understood by nonspecialists.

* 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.

* A self-contained appendix provides a comprehensive review of concepts from linear algebra, multivariate calculus, and systems of ordinary differential equations.

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.

Table of contents (9 chapters)

  • Introduction

    Chirikjian, Gregory S.

    Pages 1-29

  • Gaussian Distributions and the Heat Equation

    Chirikjian, Gregory S.

    Pages 31-61

  • Probability and Information Theory

    Chirikjian, Gregory S.

    Pages 63-99

  • Stochastic Differential Equations

    Chirikjian, Gregory S.

    Pages 101-139

  • Geometry of Curves and Surfaces

    Chirikjian, Gregory S.

    Pages 141-192

Buy this book

eBook $19.99
$54.99 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-0-8176-4803-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $29.99
$69.99 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-0-8176-4802-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Models, Information Theory, and Lie Groups, Volume 1
Book Subtitle
Classical Results and Geometric Methods
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4803-9
DOI
10.1007/978-0-8176-4803-9
Hardcover ISBN
978-0-8176-4802-2
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XXII, 383
Number of Illustrations and Tables
13 b/w illustrations
Topics