This monograph offers a comprehensive survey on the research on birth death processes and Markov chains with conitnuous time parameters. Never before has a systematic approach to the subject been made. Many new results, methods and information come to light and are presented for the first time in a compact, accessible volume. For the English edition manynew results have been added, the book was brought up-to-date and two new chapters were written specifically for this edition. A comprehensive survey of the area of birth and death processes and Markov chains with continuous time parameters. For the English edition, many new results have been added, bringing the book up-to-date and two new chapters were written, specifically for this edition.

zlibzh/no-category/Zikun Wang，Xiangqun Yang, Wang Zikun, Yang Xiangqun, Tzu-kʻun Wang/Birth and Death Processes and Markov Chains_44339288.pdf

Tzu-kʻun Wang, Wang, Zikun., Yang, Xiangqun

Zikun Wang, Xiangqun Yang

Springer Spektrum. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Copernicus

Telos

Rev. ed., Berlin, New York, Beijing, Germany, 1992

United States, United States of America

China, People's Republic, China

Berlin, Heidelberg, 1992

Germany, Germany

England, 1992

April 1993

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Includes bibliographical references (p. 352-359) and index.

Contains Bibliographical references at p. 353-359.
Contains Index.

Type: 当代图书

Bookmarks:
1. (p1) Chapter\ Ⅰ\ \ General\ Concepts\ of\ Stochastic\ Processes
1.1. (p1) 1.1 Definition of Stochastic Processes
1.2. (p6) 1.2 Separability of Stochastic Processes
1.3. (p11) 1.3 Measurability of Stochastic Processes
1.4. (p15) 1.4 Conditional Probabilities and Conditional Mathematical Expectations
1.5. (p20) 1.5 Markov Property
1.6. (p23) 1.6 Transition Probabilities
2. (p29) Chapter Ⅱ Analytic Theory of Markov Chains
2.1. (p29) 2.1 General Properties of Measurable Transition Matrices
2.2. (p34) 2.2 Differentiability of Standard Transition Matrices
2.3. (p49) 2.3 Backward and Forward Differential Equations
2.4. (p61) 2.4 Standard Generalized Transition Matrices
2.5. (p66) 2.5 Resolvent Matrices
2.6. (p72) 2.6 The Minimal Q-Resolvent Matrices
2.7. (p74) 2.7 Properties of the Minimal Q-Resolvent Matrix
2.8. (p78) 2.8 Exit Families and Entrance Families
2.9. (p83) 2.9 General Forms of Q-Resolvent Matrices
2.10. (p86) 2.10 Construction of Q-Resolvent Matrices in Simple Cases
3. (p96) Chapter Ⅲ Properties of Sample Functions
3.1. (p96) 3.1 Sets of Constancy and Intervals of Constancy
3.2. (p102) 3.2 Right Lower Semi-Continuity;Canonical Chains
3.3. (p108) 3.3 Strong Markov Property
4. (p112) Chapter Ⅳ Some Topics in Markov Chains
4.1. (p112) 4.1 Zero-One Laws
4.2. (p121) 4.2 Recurrence and Excessive Functions
4.3. (p127) 4.3 Distributions of Stochastic Functionals of Integral Type
4.4. (p138) 4.4 Embedding Problem
5. (p146) Chapter Ⅴ Basic Theory of Birth and Death Processes
5.1. (p146) 5.1 Probabilistic Meanings of Numerical Characteristics
5.2. (p154) 5.2 Random Functionals of Upward Integral Type
5.3. (p167) 5.3 First Entrance Time and Sojourn Time
5.4. (p174) 5.4 Random Functionals of Downward Integral Type
5.5. (p183) 5.5 Solutions of Several Types of Kolmogorov Equations and Stationary Distributions
5.6. (p194) 5.6 Some Applications of Birth and Death Processes
6. (p199) Chapter Ⅵ Construction Theory of Birth and Death Processes
6.1. (p199) 6.1 Transformations of Doob Processes
6.2. (p207) 6.2 The Necessary and Sufficient Condition that a Process Cannot Enter Continuously
6.3. (p211) 6.3 Transformation of General Q- Processes into Doob Processes
6.4. (p215) 6.4 Construction of Q-Processes for S<∞
6.5. (p225) 6.5 Characteristic Sequences and Classification of Birth and Death Processes
6.6. (p234) 6.6 Fundamental Theorem
6.7. (p237) 6.7 Another Construction of Q-Processes in Case S=∞
6.8. (p240) 6.8 Ergodic Property and Zero-One Laws
7. (p244) Chapter Ⅶ Analytical Construction of Birth and Death Processes
7.1. (p244) 7.1 Natural Scale and Canonical Measure
7.2. (p245) 7.2 Second Order Difference Operators
7.3. (p249) 7.3 The Solution to the Equation λu-Dμu+=O
7.4. (p251) 7.4 Construction of the Minimal Solution
7.5. (p254) 7.5 Some Lemmas
7.6. (p258) 7.6 Construction of the Q-Resolvent Matrix of B-Type
7.7. (p259) 7.7 Construction of the Q-Resolvent Matrix of F-Type
7.8. (p261) 7.8 Construction of Q-Resolvent Matrices Neither of B-Type nor of F-Type:In the Case of Linear Dependence
7.9. (p265) 7.9 Construction of Q-Resolvent Matrices Neither of B-Type nor of F-Type:In the Case of Linear Independence
7.10. (p275) 7.10 The Conditions for αφ(λ)？l
7.11. (p277) 7.11 Birth and Death Processes of Probability
7.12. (p286) 7.12 Relation Between Probabilistic and Analytic Constructions
7.13. (p290) 7.13 Properties of a Process on Its First Point of Flying Leap
7.14. (p292) 7.14 Invariant Measure
8. (p294) Chapter Ⅷ Bilateral Birth and Death Processes
8.1. (p294) 8.1 Numerical Characteristics and Classification of Boundary Points
8.2. (p295) 8.2 Solutions to the Equation λu-Dμu+=0
8.3. (p299) 8.3 The Minimal Solution
8.4. (p301) 8.4 Representations for Exit and Entrance Families
8.5. (p305) 8.5 γ1 is Entrance or Natural and γ2 is Regular or Exit
8.6. (p306) 8.6 Both γ1 and γ1 are Regular or Exit
8.7. (p309) 8.7 Conditions for αφ(λ)？l
8.8. (p311) 8.8 Properties of Boundaries
8.9. (p318) 8.9 Recurrence and Ergodicity
9. (p324) Appendix Ⅰ Excessive Functions of Markov Chains with Discrete Time
9.1. (p324) 0.1 Potential and Excessive Functions
9.2. (p333) 0.2 Limit Theorems on Excessive Functions
10. (p346) Appendix Ⅱ λ-Systems and the ？-System Method
11. (p349) Annotations on the History of the Contents of Each Section

Type: modern

- General Concepts of Stochastic Processes.
- Analytic Theory of Markov Chains.
- Properties of Sample Functions.
- Some Topics in Markov Chains.
- Basic Theory of Birth and Death Processes.
- Construction Theory of Birth and Death Processes.
- Analytical Construction of Birth and Death Processes.
- Bilateral Birth and Death Processes.
- Excessive Functions of Markov Chains with Discrete Time.
- Systems and the System Method.
- Annotations on the History of the contents of Each Section.

2024-06-13