Diffusions, Markov Processes, and Martingales: Volume 1, Foundations (Paperback, 2 Revised edition)

Some frequently used notation; 1. Brownian motion; Part I. Introduction: 2. Basics about Brownian motion; 3. Brownian motion in higher dimensions; 4. Gaussian processes and Levy processes; Part II. Some Classical Theory: 5. Basic measure theory; 6. Basic probability theory; 7. Stochastic processes; 8. Discrete-parameter martingale theory; 9. Continuous-parameter martingale theory; 10. Probability measure on Lusin spaces; Part III. Markov Processes: 11. Transition functions and resolvents; 12. Feller?Dynkin processes; 13. Additive functionals; 14. Approach to ray processes: the Martin boundary; 15. Ray processes; 16. Applications; References; Index.