Multidimensional diffusion processes

By: Daniel W. StroockContributor(s): S. R. Srinivasa VaradhanMaterial type: TextTextPublication details: Heidelberg: Springer-Verlag [c1979]Description: 338 pISBN: 9783540289982Subject(s): MathematicsLOC classification: QA274.75Online resources: Click here to access online
Contents:
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
Summary: 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
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 5 QA274.75 (Browse shelf (Opens below)) Available Invoice no. IN 980 ; Date: 22-10-2019 02215
Total holds: 0

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

There are no comments on this title.

to post a comment.