Daniel W. Stroock
Multidimensional diffusion processes - Heidelberg: Springer-Verlag [c1979] - 338 p
1. Introduction
2. Preliminary Material: Extension Theorems, Martingales, and Compactness
3. Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure
4. Parabolic Partial Differential Equations
5. The Stochastic Calculus of Diffusion Theory
6. Stochastic Differential Equations
7. The Martingale Formulation
8. Uniqueness
9. Itô’s Uniqueness and Uniqueness to the Martingale Problem
10. Some Estimates on the Transition Probability Functions
11. Explosion
12. Limit Theorems
13. The Non-unique Case
This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. The reader must be familiar with standard probability theory and measure theory which are summarized at the beginning of the book. This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view. --- summary provided by publisher
9783540289982
Mathematics
QA274.75
Multidimensional diffusion processes - Heidelberg: Springer-Verlag [c1979] - 338 p
1. Introduction
2. Preliminary Material: Extension Theorems, Martingales, and Compactness
3. Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure
4. Parabolic Partial Differential Equations
5. The Stochastic Calculus of Diffusion Theory
6. Stochastic Differential Equations
7. The Martingale Formulation
8. Uniqueness
9. Itô’s Uniqueness and Uniqueness to the Martingale Problem
10. Some Estimates on the Transition Probability Functions
11. Explosion
12. Limit Theorems
13. The Non-unique Case
This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. The reader must be familiar with standard probability theory and measure theory which are summarized at the beginning of the book. This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view. --- summary provided by publisher
9783540289982
Mathematics
QA274.75