MARC details
| 000 -LEADER |
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| fixed length control field |
03368 a2200373 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319057224 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-3-319-05723-1 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)883025069 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA274.7 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.233 |
| 090 ## - LOCALLY ASSIGNED LC-TYPE CALL NUMBER (OCLC); LOCAL CALL NUMBER (RLIN) |
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| -- |
32056 |
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32056 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Zaharopol, Radu |
| 245 10 - TITLE STATEMENT |
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| Title |
Invariant probabilities of transition functions |
| Statement of responsibility, etc. |
Radu Zaharopol |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 389 p. |
| Dimensions |
24 cm |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Probability and its applications, |
| International Standard Serial Number |
1431-7028. |
| 546 ## - LANGUAGE NOTE |
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| Language note |
eng |
| 500 ## - GENERAL NOTE |
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| General note |
Bibliografie p. 375<br/>Index p. 381 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Introduction -- 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 ## - SUMMARY, ETC. |
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| Summary, etc. |
The 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Markov processes. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Ergodic theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Invariants. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Operator Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Dynamical Systems and Ergodic Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Probability Theory and Stochastic Processes. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Potential Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Measure and Integration. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICS / Probability & Statistics / General |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 655 #0 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Probability and its applications (Springer-Verlag) |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Institution code [OBSOLETE] |
IMAR |
| Koha item type |
Carti |
| Call number prefix |
519.233 |
| Serial record flag |
EP |