Author | Freedman, David. author |
---|---|
Title | Brownian Motion and Diffusion [electronic resource] / by David Freedman |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6574-1 |
Descript | 231 p. online resource |
1. Brownian Motion -- 1. Introduction -- 2. Foundations -- 3. Strong Markov and Reflection -- 4. Sample Function Properties -- 5. Strassenโs Law of the Iterated Logarithm -- 6. The Skorokhod Representation -- 7. Donskerโs Invariance Principle -- 8. Strassenโs Invariance Principle -- 9. Lindebergโs Theorem for Martingales -- 10. Central Limit Theorem for Random Sums -- 11. Waldโs Identity -- 2. Diffusion -- 1. Introduction -- 2. Regularity -- 3. Scale -- 4. Semigroups -- 5. Greenโs Function -- 6. Speed Measure -- 7. Infinitesimal Generator -- 8. Brownian Local Time -- 9. Transformation of Time -- 10. Diffusion Local Time -- 11. First Examples -- 12. An Example of Feller and McKean -- 13. An Example of Breiman -- 14. A Generalization -- 15. Weak Markov Processes -- 3. Appendix -- 1. Notation -- 2. Numbering -- 3. Bibliography -- 4. The Abstract Lebesgue Integral -- 5. Atoms -- 6. Independence -- 7. Conditioning -- 8. Martingales -- 9. Metric Spaces -- 10. Regular Conditional Distributions -- 11. The Kolmogorov Consistency Theorem -- 12. The Diagonal Argument -- 13. Classical Lebesgue Measure -- 14. Real Variables -- 15. Absolute Continuity -- 16. Convex Functions -- 17. Complex Variables -- Symbol Finder