Stochastic Models, Information Theory, and Lie Groups, Volume 2 (eBook)

Analytic Methods and Modern Applications

Gregory S. Chirikjian (Autor)

eBook Download: PDF

2011 | 2012. Auflage
XXVII, 435 Seiten
Birkhauser Boston (Verlag)
978-0-8176-4944-9 (ISBN)

Infos

This two-volume set covers stochastic processes, information theory and Lie groups in a unified setting, bridging topics rarely studied together. The emphasis is on using stochastic, geometric, and group-theoretic concepts for modeling physical phenomena.

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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.

Inhalt

Lie Groups I: Introduction and Examples.- Lie Groups II: Differential Geometric Properties.- Lie Groups III: Integration, Convolution, and Fourier Analysis.- Variational Calculus on Lie Groups.- Statistical Mechanics and Ergodic Theory.- Parts Entropy and the Principal Kinematic Formula.- Estimation and Multivariate Analysis in R^n.- Information, Communication, and Group Therapy.- Algebraic and Geometric Coding Theory.- Information Theory on Lie Groups.- Stochastic Processes on Lie Groups.- Locomotion and Perception as Communication over Principal Fiber Bundles; and A Survey of Additional Applications.

Produkt-Details

• Erscheint lt. Verlag: 16.11.2011
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: biomolecular information theory • coding problems on Lie groups • conformational fluctuations of DNA • differentiable manifolds • differential forms • diffusion processes, motion groups • g • Gaussian Distributions, Heat Equation • geometric robotic manipulator • information theory and group theory • infotaxis • Lie groups • rotational Brownian motion • Shannon's information theory • statistical mechanics, ergodic theory • stochastic processes on Lie groups
• ISBN-10: 0-8176-4944-1 / 0817649441
• ISBN-13: 978-0-8176-4944-9 / 9780817649449