Stochastic Models, Information Theory, and Lie Groups, Volume 1 [electronic resource] : Classical Results and Geometric Methods / by Gregory S. Chirikjian.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Applied and Numerical Harmonic Analysis: Publisher: Boston : Birkhäuser Boston, 2009Description: XXII, 383 p. 13 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817648039Subject(s): Mathematics | Topological groups | Lie groups | Functions of complex variables | Applied mathematics | Engineering mathematics | Differential geometry | Probabilities | Mathematics | Probability Theory and Stochastic Processes | Functions of a Complex Variable | Applications of Mathematics | Appl.Mathematics/Computational Methods of Engineering | Differential Geometry | Topological Groups, Lie GroupsAdditional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online
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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.
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.