LEADER 05123nam 22007935 450 001 9910299991203321 005 20220413201221.0 010 $a3-319-05723-5 024 7 $a10.1007/978-3-319-05723-1 035 $a(CKB)3710000000143804 035 $a(EBL)1782867 035 $a(SSID)ssj0001276243 035 $a(PQKBManifestationID)11836033 035 $a(PQKBTitleCode)TC0001276243 035 $a(PQKBWorkID)11238630 035 $a(PQKB)11641795 035 $a(MiAaPQ)EBC1782867 035 $a(DE-He213)978-3-319-05723-1 035 $a(PPN)179767178 035 $a(EXLCZ)993710000000143804 100 $a20140627d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInvariant probabilities of transition functions$b[electronic resource] /$fby Radu Zaharopol 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (405 p.) 225 1 $aProbability and Its Applications,$x1431-7028 300 $aDescription based upon print version of record. 311 $a1-322-13468-5 311 $a3-319-05722-7 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications. 410 0$aProbability and Its Applications,$x1431-7028 606 $aOperator theory 606 $aDynamics 606 $aErgodic theory 606 $aProbabilities 606 $aPotential theory (Mathematics) 606 $aMeasure theory 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aOperator theory. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aProbabilities. 615 0$aPotential theory (Mathematics). 615 0$aMeasure theory. 615 14$aOperator Theory. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aProbability Theory and Stochastic Processes. 615 24$aPotential Theory. 615 24$aMeasure and Integration. 676 $a519.233 700 $aZaharopol$b Radu$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721622 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299991203321 996 $aInvariant probabilities of transition functions$91410297 997 $aUNINA