LEADER 05691nam 22006855 450 001 9910633936303321 005 20230515132124.0 010 $a3-031-00943-6 024 7 $a10.1007/978-3-031-00943-3 035 $a(MiAaPQ)EBC7151488 035 $a(Au-PeEL)EBL7151488 035 $a(CKB)25510431700041 035 $a(DE-He213)978-3-031-00943-3 035 $a(PPN)267813503 035 $a(EXLCZ)9925510431700041 100 $a20221201d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStationary Processes and Discrete Parameter Markov Processes /$fby Rabi Bhattacharya, Edward C. Waymire 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (449 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v293 311 08$aPrint version: Bhattacharya, Rabi Stationary Processes and Discrete Parameter Markov Processes Cham : Springer International Publishing AG,c2023 9783031009419 320 $aIncludes bibliographical references and index. 327 $aSymbol Definition List -- 1. Fourier Analysis: A Brief -- 2. Weakly Stationary Processes and their Spectral Measures -- 3. Spectral Representation of Stationary Processes -- 4. Birkhoff?s Ergodic Theorem -- 5. Subadditive Ergodic Theory -- 6. An Introduction to Dynamical Systems -- 7. Markov Chains -- 8. Markov Processes with General State Space -- 9. Stopping Times and the Strong Markov Property -- 10. Transience and Recurrence of Markov Chains -- 11. Birth?Death Chains -- 12. Hitting Probabilities & Absorption -- 13. Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition -- 14. The Central Limit Theorem for Markov Chains by Renewal Decomposition -- 15. Martingale Central Limit Theorem -- 16. Stationary Ergodic Markov Processes: SLLN & FCLT -- 17. Linear Markov Processes -- 18. Markov Processes Generated by Iterations of I.I.D. Maps -- 19. A Splitting Condition and Geometric Rates of Convergence to Equilibrium -- 20. Irreducibility and Harris Recurrent Markov Processes -- 21. An Extended Perron?Frobenius Theorem and Large Deviation Theory for Markov Processes -- 22. Special Topic: Applications of Large Deviation Theory -- 23. Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities -- 24. Special Topic: More on Coupling Methods and Applications -- 25. Special Topic: An Introduction to Kalman Filter -- A. Spectral Theorem for Compact Self-Adjoint Operators and Mercer?s Theorem -- B. Spectral Theorem for Bounded Self-Adjoint Operators -- C. Borel Equivalence for Polish Spaces -- D. Hahn?Banach, Separation, and Representation Theorems in Functional Analysis -- References -- Author Index -- Subject Index. 330 $aThis textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff?s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth?death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v293 606 $aStochastic processes 606 $aMarkov processes 606 $aDistribution (Probability theory) 606 $aProbabilities 606 $aStochastic Processes 606 $aMarkov Process 606 $aDistribution Theory 606 $aProbability Theory 606 $aProcessos estocāstics$2thub 608 $aLlibres electrōnics$2thub 615 0$aStochastic processes. 615 0$aMarkov processes. 615 0$aDistribution (Probability theory). 615 0$aProbabilities. 615 14$aStochastic Processes. 615 24$aMarkov Process. 615 24$aDistribution Theory. 615 24$aProbability Theory. 615 7$aProcessos estocāstics 676 $a780 700 $aBhattacharya$b R. N$g(Rabindra Nath),$f1937-$0102761 702 $aWaymire$b Edward C. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910633936303321 996 $aStationary processes and discrete parameter Markov processes$93084231 997 $aUNINA