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LEADER: 03805nam a22004935a 4500
001 014106273-8
005 20140808190850.0
008 140627s2014 gw | s ||0| 0|eng d
020 $a9783319057231
020 $a9783319057231
020 $a9783319057224
024 7 $a10.1007/978-3-319-05723-1$2doi
035 $a(Springer)9783319057231
040 $aSpringer
050 4 $aQA329-329.9
072 7 $aPBKF$2bicssc
072 7 $aMAT037000$2bisacsh
082 04 $a515.724$223
100 1 $aZaharopol, Radu,$eauthor.
245 10 $aInvariant Probabilities of Transition Functions /$cby Radu Zaharopol.
264 1 $aCham :$bSpringer International Publishing :$bImprint: Springer,$c2014.
300 $aXVIII, 389 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aProbability and Its Applications,$x1431-7028
505 0 $aIntroduction -- 1.Transition Probabilities -- 2.Transition Functions -- 3.Vector Integrals and A.E. Convergence -- 4.Special Topics -- 5.The KBBY Ergodic Decomposition, Part I -- 6.The KBBY Ergodic Decomposition, Part II -- 7.Feller Transition Functions -- Appendices: A.Semiflows and Flows: Introduction -- B.Measures and Convolutions -- Bibliography -- Index.
520 $aThe structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.
650 20 $aOperator theory.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aPotential theory (Mathematics)
650 0 $aMathematics.
650 0 $aDifferentiable dynamical systems.
650 0 $aOperator theory.
650 24 $aDynamical Systems and Ergodic Theory.
650 24 $aProbability Theory and Stochastic Processes.
650 24 $aPotential Theory.
650 24 $aMeasure and Integration.
776 08 $iPrinted edition:$z9783319057224
830 0 $aProbability and Its Applications.
988 $a20140702
906 $0VEN