國立高雄大學圖資館 |

Language: English

Back

Stationary processes and discrete parameter Markov processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stationary processes and discrete parameter Markov processesby Rabi Bhattacharya, Edward C. Waymire.
Author:	Bhattacharya, R. N.
other author:	Waymire, Edward C.
Published:	Cham :Springer International Publishing :2022.
Description:	xvii, 449 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes.
Online resource:	https://doi.org/10.1007/978-3-031-00943-3
ISBN:	9783031009433$q(electronic bk.)

Stationary processes and discrete parameter Markov processes
Bhattacharya, R. N.

Stationary processes and discrete parameter Markov processes[electronic resource] /by Rabi Bhattacharya, Edward C. Waymire. - Cham :Springer International Publishing :2022. - xvii, 449 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2932197-5612 ;. - Graduate texts in mathematics ;129..

Symbol 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.

This 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.

ISBN: 9783031009433$q(electronic bk.)

Standard No.: 10.1007/978-3-031-00943-3doiSubjects--Topical Terms:

181874
Stochastic processes.

LC Class. No.: QA274 / .B488 2022

Dewey Class. No.: 519.23

Stationary processes and discrete parameter Markov processes
LDR:04486nmm a2200361 a 4500 001 633551
003 DE-He213
005 20221201222508.0
006 m d
007 cr nn 008maaau
008 230511s2022 sz s 0 eng d
020 $a 9783031009433$q(electronic bk.)
020 $a 9783031009419$q(paper)
024 7 $a 10.1007/978-3-031-00943-3 $2 doi
035 $a 978-3-031-00943-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274 $b .B488 2022
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.23 $2 23
090 $a QA274 $b .B575 2022
100 1 $a Bhattacharya, R. N. $3 939509
245 1 0 $a Stationary processes and discrete parameter Markov processes $h [electronic resource] / $c by Rabi Bhattacharya, Edward C. Waymire.
260 $a Cham : $c 2022. $b Springer International Publishing : $b Imprint: Springer,
300 $a xvii, 449 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 293
505 0 $a Symbol 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.
520 $a This 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.
650 0 $a Stochastic processes. $3 181874
700 1 $a Waymire, Edward C. $3 245505
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-031-00943-3
950 $a Mathematics and Statistics (SpringerNature-11649)