Editorial Board
S. Axler F. W Gehring K. A. Ribet

186 Pages

 

Preface. . . . . . . . . . . . . . . . . . . . . .

Chapter 1 Random Walks A Good Place to Begin . . . . . .
1.1. Nearest Neighbor Random Walks on Z . . .
1.1.1. Distribution at Time n . . . . . . . . . . . .. ...
1.1.2. Passage Times via the Reflection Principle . .. ....
1.1.3. Some Related Computations . . . .. ... . . .
1.1.4. Time of First Return ......... .....
1.1.5. Passage Times via Functional Equations . . . .
1.2. Recurrence Properties of Random Walks ... ......
1.2.1. Random Walks on Zd . . . . . . . . . . . . . . . . . .
1.2.2. An Elementary Recurrence Criterion. . . . . . . . . . . .
1.2.3. Recurrence of Symmetric Random Walk in Z2 .....
1.2.4. Transience in Z3 ... ... ............
1.3. Exercises . . . . . . . . . . . .

Chapter 2 Doeblin's Theory for Markov Chains .......
2.1. Some Generalities ..............
2.1.1. Existence of Markov Chains .........
2.1.2. Transition Probabilities & Probability Vectors
2.1.3. Transition Probabilities and Functions
2.1.4. The Markov Property. '"
2.2. Doeblin's Theory . . . . . . . . .
2.2.1. Doeblin's Basic Theorem .........
2.2.2. A Couple of Extensions . . . . . . . . . . . . . . .
2.3. Elements of Ergodic Theory .
2.3.1. The Mean Ergodic Theorem . . .
2.3.2. Return Times . . .. ...
2.3.3. Identification of 7r . . . . . . . .
2.4. Exercises . . .. ....

Chapter 3 More about the Ergodic Theory of Markov Chains 45
3.1. Classification of States . . . . . . . . . . . . . . . 46
3.1.1. Classification, Recurrence, and Transience . .. .... 46
3.1.2. Criteria for Recurrence and Transience ......... 48
3.1.3. Periodicity . . . . . . . . . . . . . 51
3.2. Ergodic Theory without Doeblin . 53
3.2.1. Convergence of Matrices . . . 53

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[此贴子已经被作者于2008-7-13 14:28:26编辑过]