Diffusions, Markov Processes, and Martingales

Klappentext Now available in paperback for the first time; essential reading for all students of probability theory. Zusammenfassung Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. Together with its companion volume, it helps equip graduate students for research into a subject of great intrinsic interest and wide application. Inhaltsverzeichnis 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.

Zusammenfassung
Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. Together with its companion volume, it helps equip graduate students for research into a subject of great intrinsic interest and wide application.

Inhalt
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 Lévy 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.

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