Stochastic Models, Information Theory, and Lie Groups, Volume 1: Classical Results and Geometric Methods

ISBN-13: 9780817648022 / Angielski / Twarda / 2009 / 383 str.

Gregory S. Chirikjian

Opis

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups 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.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. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Spis treści

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.

Blurb

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.