04190nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137082001200172100003600184245016300220264004200383300004400425336002600469337002600495338003600521347002400557490004400581505025700625520217400882650001703056650001803073650002303091650003903114650002603153650002903179650001703208650003303225650005903258650003203317650004903349650003803398650003703436710003403473773002003507776003603527830004403563856010103607978-0-8176-4803-9DE-He21320260521092031.0cr nn 008mamaa100715s2009    xxu|    s    |||| 0|eng d  a9780817648039  a997808176480397 a10.1007/978-0-8176-4803-92doi04a5192231 aChirikjian, Gregory S.eauthor.10aStochastic Models, Information Theory, and Lie Groups, Volume 1h[electronic resource] :bClassical Results and Geometric Methods /cby Gregory S. Chirikjian. 1aBoston :bBirkhäuser Boston,c2009.  aXXII, 383p. 13 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis0 aGaussian 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.  aThe 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. 0aMATHEMATICS. 0aGROUP THEORY. 0aHARMONIC ANALYSIS. 0aDISTRIBUTION (PROBABILITY THEORY). 0aMATHEMATICAL PHYSICS. 0aENGINEERING MATHEMATICS.14aMATHEMATICS.24aAPPLICATIONS OF MATHEMATICS.24aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.24aABSTRACT HARMONIC ANALYSIS.24aPROBABILITY THEORY AND STOCHASTIC PROCESSES.24aGROUP THEORY AND GENERALIZATIONS.24aMATHEMATICAL METHODS IN PHYSICS.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817648022 0aApplied and Numerical Harmonic Analysis40uhttp://dx.doi.org/10.1007/978-0-8176-4803-9zVer el texto completo en las instalaciones del CICY