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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.
List of contents
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.- Numerical Group Representation Theory.-Rotational and Rigid-Body Diffusion.- Kinematic Covariance Propagation.- Biomolecular Conformation and Information Theory.- Infotaxis.- A Survey of Additional Applications.- Summary.- Inequalities, Convexity, and Rearrangements.- Index.
Summary
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.
