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.