000			03909nam a22004215i 4500
001			978-0-387-36081-2
003			DE-He213
005			20250710083956.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387360812 _a99780387360812
024	7		_a10.1007/0-387-36081-6 _2doi
082	0	4	_a519.2 _223
100	1		_aKalpazidou, Sophia L. _eauthor.
245	1	0	_aCycle Representations of Markov Processes _h[recurso electrónico] / _cby Sophia L. Kalpazidou.
250			_aSecond Edition.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXX, 301 p. 17 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aStochastic Modelling and Applied Probability, _x0172-4568 ; _v28
505	0		_aFundamentals of the Cycle Representations of Markov Processes -- Directed Circuits -- Genesis of Markov Chains by Circuits: The Circuit Chains -- Cycle Representations of Recurrent Denumerable Markov Chains -- Circuit Representations of Finite Recurrent Markov Chains -- Continuous Parameter Circuit Processes with Finite State Space -- Spectral Theory of Circuit Processes -- Higher-Order Circuit Processes -- Cycloid Markov Processes -- Markov Processes on Banach Spaces on Cycles -- The Cycle Measures -- Wide-Ranging Interpretations of the Cycle Representations of Markov Processes -- Applications of the Cycle Representations -- Stochastic Properties in Terms of Circuits -- Lévy's Theorem Concerning Positiveness of Transition Probabilities -- The Rotational Theory of Markov Processes.
520			_aThis book is a prototype providing new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the Markov process. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. In particular, it provides an entirely new approach to infinite electrical networks and their applications in topics as diverse as random walks, the classification of Riemann surfaces, and to operator theory. The second edition of this book adds new advances to many directions, which reveal wide-ranging interpretations of the cycle representations like homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The versatility of these interpretations is consequently motivated by the existence of algebraic-topological principles in the fundamentals of the cycle representations. This book contains chapter summaries as well as a number of detailed illustrations. Review of the earlier edition: "This is a very useful monograph which avoids ready ways and opens new research perspectives. It will certainly stimulate further work, especially on the interplay of algebraic and geometrical aspects of Markovian dependence and its generalizations." Math Reviews.
650		0	_aMATHEMATICS.
650		0	_aDISTRIBUTION (PROBABILITY THEORY).
650	1	4	_aMATHEMATICS.
650	2	4	_aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387291666
830		0	_aStochastic Modelling and Applied Probability, _x0172-4568 ; _v28
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-36081-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57480 _d57480