Synopses & Reviews
A wide variety of problems in engineering and applied science can be formulated as diffusion processes on motion groups. Often, underlying phenomena associated with diffusion processes on motion groups have been rediscovered in the context of each new application area studied, and ad-hoc solution techniques have been derived each time. This textbook takes the unique perspective of presenting underlying equations that are the same in a variety of fields to develop an elegant solution technique based on concepts from noncommutative harmonic analysis.
Key features and topics:
* Includes a review of stochastic processes and Lie groups in an accessible way for applied mathematicians, scientists, and engineers.
* Extensive exercises make the work suitable as a textbook for use in graduate courses that emphasize either applied stochastic processes or group theory.
* The differential geometry of matrix Lie groups is reviewed in a concrete way.
* The Fokker-Planck Equation for diffusion processes on Lie groups is derived in a way that can be understood by nonspecialists.
* The representation theory and Fourier analysis associated with rotation and Euclidean motion groups are reviewed in different parameterizations.
* Equations describing degenerate diffusions on motion groups arising in a variety of application areas are described and solved; these areas include phase noise in coherent optical communication systems, statistical mechanics of semi-flexible polymers, workspace densities of robotic manipulators and steerable needles, and bacterial chemotaxis.
* Concrete presentation, making it easy for readers to obtain numerical solutions for their own problems.
Stochastic Models and Lie Groups will be of interest to graduate students and researchers working in applied mathematics, the sciences, and engineering.
Synopsis
This unique two-volumeset presentsthe subjects of stochastic processes, information theory, and Lie groupsin 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.
Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitionersworking in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
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Synopsis
The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume
Synopsis
This unique two-volume
Synopsis
Tools and methods from stochastic processes, information theory, and Lie groups are used in a wide variety of problems in engineering and the physical sciences. Featuring extensive exercises and applications, this two-volume set presents these topics in a uniquely unified setting.
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Synopsis
This unique two-volume
Table of Contents
ANHA Series Preface.- Preface.- Introduction.- Gaussian Distributions and the Heat Equation.- Probability and Information Theory.- Stochastic Differential Equations.- Geometry of Curves and Surfaces.- Differential Forms.- Polytopes and Manifolds.- Stochastic Processes on Manifolds.- Summary.- Appendix: Review of Linear Algebra, Vector Calculus, and Systems Theory.- Index.