000			04328nam a22005295i 4500
001			978-0-8176-4803-9
003			DE-He213
005			20251006084439.0
007			cr nn 008mamaa
008			100715s2009 xxu| s |||| 0|eng d
020			_a9780817648039
020			_a99780817648039
024	7		_a10.1007/978-0-8176-4803-9 _2doi
082	0	4	_a519 _223
100	1		_aChirikjian, Gregory S. _eauthor.
245	1	0	_aStochastic Models, Information Theory, and Lie Groups, Volume 1 _h[electronic resource] : _bClassical Results and Geometric Methods / _cby Gregory S. Chirikjian.
264		1	_aBoston : _bBirkhäuser Boston, _c2009.
300			_aXXII, 383p. 13 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_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.
520			_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.
650		0	_aMATHEMATICS.
650		0	_aGROUP THEORY.
650		0	_aHARMONIC ANALYSIS.
650		0	_aDISTRIBUTION (PROBABILITY THEORY).
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aENGINEERING MATHEMATICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.
650	2	4	_aABSTRACT HARMONIC ANALYSIS.
650	2	4	_aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650	2	4	_aGROUP THEORY AND GENERALIZATIONS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817648022
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4803-9 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59795 _d59795