Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Chirikjian, Gregory S.
Titre(s) : Stochastic models, information theory, and lie groups, volume 1 [Texte électronique] : classical results and geometric methods / by Gregory S. Chirikjian
Publication : Boston : Birkhäuser Boston : Springer e-books, 2009
Description matérielle : 1 online resource
Collection : Applied and Numerical Harmonic Analysis
Note(s) : Titre provenant de l'écran-titre. - Numerisation de l'édition de : [s.l.] : Springer science + Business Media. 2009. - Bibliogr. Index
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
Sujet(s) : Théorie des groupes
Analyse harmonique (mathématiques)
Distribution (théorie des probabilités)
Physique mathématique
Mathématiques de l'ingénieur
Groupes topologiques
Groupes de Lie
Fonctions d'une variable complexe
Mathématiques
Probabilités
Indice(s) Dewey :
519.2 (23e éd.) = Probabilités
Identifiants, prix et caractéristiques : ISBN 9780817648039
Identifiant de la notice : ark:/12148/cb446518089
Notice n° :
FRBNF44651808
(notice reprise d'un réservoir extérieur)