Stochastic Models, Information Theory, and Lie Groups, Volume 2 [electronic resource] : Analytic Methods and Modern Applications / by Gregory S. Chirikjian.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Applied and Numerical Harmonic Analysis: Publisher: Boston : Birkhäuser Boston, 2012Description: XXVII, 435 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817649449Subject(s): Mathematics | Topological groups | Lie groups | Applied mathematics | Engineering mathematics | Differential geometry | Probabilities | Physics | Mathematics | Applications of Mathematics | Appl.Mathematics/Computational Methods of Engineering | Differential Geometry | Probability Theory and Stochastic Processes | Topological Groups, Lie Groups | Mathematical Methods in PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: T57-57.97Online resources: Click here to access online
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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.
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.