多維擴散過程

Frequently Used Notation
Chapter 0 Introduction
Chapter 1 Preliminary Material：Extension Theorems，Martingales，and Compactness
1．0 Introduction
1．1 Weak Convergence．Conditional Probability Distributions and Extension Theorems
1．2 Martingales．
1．3 The Space c([0，0)；R)
1．4 Martingales and Compactness
1．5 Exercises
Chapter 2 Markov Processes，Regularity of Their Sample Paths，and the Wiener Measure．
2．1 Regularity of Paths
2．2MarkOVProcesses andTransitionProbabilities
2．3 Wiener Measure
2．4 Exercises
Chapter 3 ParabolicPartialDifferentialEquations
3．1 The Maximum Principle．
3．2 Existence Theorems
3．3 Exercises
Chapter 4 The Stochastic Calculus of Di斤usion Theory
4．1 Brownian Morion，
4．2 Equivalence ofCertain Martingales
4．3 It6 Processes and Stochastic Integration
4．4 It’s Formula
4．5 It Processes as Stochastic Integrals
4．6 ExerciSes
Chapter 5 Stochastic Dilierential Equations
5．0 Introduction
5．1 Existence and Uniqueness
5．2 On the Lipschitz Condition
5．3Equivalence ofDifferentChoices ofthe SquareRoot
5．4 Exercises
Chapter 6 The Martingale Formulation
6．0 Introduction
6．1 Existence
6．2 Uniqueness：Markov Property
6．3 Uniqueness：Some Examples．
6．4 Cameron．Martin．Girsanov Formula
6．5 Uniqueness：Random Time Change
6．6 Uniqueness：Localization．
6．7 Exercises
Chapter 7 Uniqueness
7．0 Introduction
7．1 Uniqueness：Local Case
7．2 Uniqueness：Global Case
7．3 ExereiSes
Chapter 8 It’S Uniqueness and Uniqueness to the Martingale Problem
8．0 Introduction．
8．I Results ofYamada and Watanabe
8．2 More 0n Itb Uniqueness
8．3 Exercises
Chapter 9 Some Estimates on the Transition Probability Functions
9．0 Introduetion
9．1 The Inhomogeneous Case
9．2 The Homogeneous Case
Chapter 10 Explosion
10．0Introduction
10．1 Locally Bounded Cocfficients
10．2ConditionsforExplosion andNon-Explosion
10．3 Exercises．
Chapter 11 Limit Theorems
11．0 Introduction
11．1 Convergence ofDiffusion Process
11．2 Convergence ofMarkov Chains to Diffusions
11．3ConvergenceofDiffusionProcesses：EllipticCase
11．4 Convergence ofTransition Probability Densities
11．5 ExerciSeS
Chapter 12 The Non—Unique Case
12．0 Introduction
12．1 Existence ofMeasurable Choices
12．2 Markov Selections
12．3 Reconstruction ofAll Solutions
12．4 Exercises
Appendix
A．0 Introduction
A．1 L Estimates for Some Singular Integral Operators
A．2 Proofofthe Main Estimate
A．3 Exercises
Bibliographical Remarks
Bibliography
Index