05053nam 22006613 450 991095632240332120231110223341.097814704681321470468131(MiAaPQ)EBC6822201(Au-PeEL)EBL6822201(CKB)20058043500041(RPAM)22487735(OCoLC)1284944707(EXLCZ)992005804350004120211209d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierErgodicity of Markov Processes Via Nonstandard Analysis1st ed.Providence :American Mathematical Society,2021.©2018.1 online resource (126 pages)Memoirs of the American Mathematical Society ;v.273Print version: Duanmu, Haosui Ergodicity of Markov Processes Via Nonstandard Analysis Providence : American Mathematical Society,c2021 9781470450021 Includes bibliographical references.Cover -- Title page -- Chapter 1. Introduction -- 1.1. Chapter Outline -- Chapter 2. Markov Processes and the Main Result -- Chapter 3. Preliminaries: Nonstandard Analysis -- 3.1. The Hyperreals -- 3.2. Nonstandard Extensions of General Metric Spaces -- Chapter 4. Internal Probability Theory -- 4.1. Product Measures -- 4.2. Nonstandard Integration Theory -- Chapter 5. Measurability of Standard Part Map -- Chapter 6. Hyperfinite Representation of a Probability Space -- Chapter 7. General Hyperfinite Markov Processes -- Chapter 8. Hyperfinite Representation for Discrete-time Markov Processes -- 8.1. General properties of the transition probability -- 8.2. Hyperfinite Representation for Discrete-time Markov Processes -- Chapter 9. Hyperfinite Representation for Continuous-time Markov Processes -- 9.1. Construction of Hyperfinite State Space -- 9.2. Construction of Hyperfinite Markov Processess -- Chapter 10. Markov Chain Ergodic Theorem -- Chapter 11. The Feller Condition -- 11.1. Hyperfinite Representation under the Feller Condition -- 11.2. A Weaker Markov Chain Ergodic Theorem -- Chapter 12. Push-down Results -- 12.1. Construction of Standard Markov Processes -- 12.2. Push down of Weakly Stationary Distributions -- 12.3. Existence of Stationary Distributions -- Chapter 13. Merging of Markov Processes -- Chapter 14. Miscellaneous Remarks -- Acknowledgement -- Bibliography -- Back Cover."The Markov chain ergodic theorem is well-understood if either the time-line or the state space is discrete. However, there does not exist a very clear result for general state space continuous-time Markov processes. Using methods from mathematical logic and nonstandard analysis, we introduce a class of hyperfinite Markov processes-namely, general Markov processes which behave like finite state space discrete-time Markov processes. We show that, under moderate conditions, the transition probability of hyperfinite Markov processes align with the transition probability of standard Markov processes. The Markov chain ergodic theorem for hyperfinite Markov processes will then imply the Markov chain ergodic theorem for general state space continuous-time Markov processes"--Provided by publisher.Memoirs of the American Mathematical Society Markov processesErgodic theoryNonstandard mathematical analysisMathematical logic and foundations -- Nonstandard models -- Nonstandard models in mathematicsmscMeasure and integration -- Miscellaneous topics in measure theory -- Nonstandard measure theorymscProbability theory and stochastic processes -- Markov processes -- Discrete-time Markov processes on general state spacesmscProbability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spacesmscMarkov processes.Ergodic theory.Nonstandard mathematical analysis.Mathematical logic and foundations -- Nonstandard models -- Nonstandard models in mathematics.Measure and integration -- Miscellaneous topics in measure theory -- Nonstandard measure theory.Probability theory and stochastic processes -- Markov processes -- Discrete-time Markov processes on general state spaces.Probability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces.519.2/3303H0528E0560J0560J25mscDuanmu Haosui1801697Rosenthal Jeffrey S281907Weiss William1801698MiAaPQMiAaPQMiAaPQBOOK9910956322403321Ergodicity of Markov Processes Via Nonstandard Analysis4347070UNINA02471nam0 22006013i 450 VAN0029092020250624104122.277N978940158232220250407d1993 |0itac50 baengNL|||| |||||i e bcrAlgorithms: Main Ideas and Applicationsby Vladimir Uspensky and Alexei SemenovDordrechtSpringerKluwer1993xii, 269 p.ill.24 cmTransl. from the Russian by A. Shen001VAN000224232001 Mathematics and its applications210 DordrechtReidel1977-2007300 L'editore varia in: Kluwer ; [poi] Springer251VAN00290921Teoriya algoritmov: osnovnye otkrytiya i prilozheniya435048703-XXMathematical logic and foundations [MSC 2020]VANC019750MF03DxxComputability and recursion theory [MSC 2020]VANC024386MF68-XXComputer science [MSC 2020]VANC019670MFAlgorithmsKW:KArithmeticKW:KBoundary Element MethodsKW:KComplexityKW:KDesignKW:KEntropyKW:KFormsKW:KHardwareKW:KInformation TheoryKW:KInformationsKW:KLogicKW:KMathematical logicKW:KNotationKW:KRandomnessKW:KSemanticsKW:KNLDordrechtVANL000068UspenskyVladimir A.VANV2461501803445SemenovAlekseĭ L.VANV2461511803446Kluwer <editore>VANV108116650Springer <editore>VANV108073650Semenov, Alekseĭ L’vovichSemenov, Alekseĭ L.VANV246152ITSOL20250829RICAhttps://doi.org/10.1007/978-94-015-8232-2E-book – Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o ShibbolethBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICAIT-CE0120VAN08NVAN00290920BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08DLOAD e-Book 11369 08eMF11369 20250611 Teoriya algoritmov: osnovnye otkrytiya i prilozheniya4350487UNICAMPANIA