扩散 马尔可夫过程和鞅 第1卷

1 (p1): CHAPTER Ⅰ．BROWNIAN MOTION
1 (p1-1): 1．INTRODUCTION
1 (p1-1-1): 1 What is Brownian motion,and why study it?
2 (p1-1-2): 2．Brownian motion as a martingale
3 (p1-1-3): 3．Brownian motion as a Gaussian process
5 (p1-1-4): 4．Brownian motion as a Markov process
7 (p1-1-5): 5 Brownian motion as a diffusion（and martingale）
10 (p1-2): 2．BASICS ABOUT BROWNIAN MOTION
10 (p1-2-1): 6 Existence and uniqueness of Brownian motion
13 (p1-2-2): 7．Skorokhod embedding
16 (p1-2-3): 8．Donsker's Invariance Principle
18 (p1-2-4): 9．Exponential martingales and first-passage distributions
19 (p1-2-5): 10．Some sample-path properties
21 (p1-2-6): 11．Quadratic variation
21 (p1-2-7): 12．The strong Markov property
25 (p1-2-8): 13．Reflection
27 (p1-2-9): 14．Reflecting Brownian motion and local time
31 (p1-2-10): 15．Kolmogorov's test
31 (p1-2-11): 16．Brownian exponential martingales and the Law of the Iterated Logarithm
36 (p1-3): 3．BROWNIAN MOTION IN HIGHER DIMENSIONS
36 (p1-3-1): 17．Some martingales for Brownian motion
38 (p1-3-2): 18．Recurrence and transience in higher dimensions
39 (p1-3-3): 19．Some applications of Brownian motion to complex analysis
43 (p1-3-4): 20．Windings of planar Brownian motion
45 (p1-3-5): 21．Multiple points,cone points,cut points
46 (p1-3-6): 22．Potential theory of Brownian motion in IRd（d≥3）
51 (p1-3-7): 23．Brownian motion and physical diffusion
55 (p1-4): 4．GAUSSIAN PROCESSES AND LEVY PROCESSES
55 (p1-4-1): Gaussian processes
55 (p1-4-1-1): 24．Existence results for Gaussian processes
59 (p1-4-1-2): 25 Continuity results
66 (p1-4-1-3): 26．Isotropic random flows
71 (p1-4-1-4): 27．Dynkin's Isomorphism Theorem
73 (p1-4-2): Lévy processes
73 (p1-4-2-1): 28．Lévy processes
80 (p1-4-2-2): 29．Fluctuation theory and Wiener-Hopf factorisation
82 (p1-4-2-3): 30．Local time of Levy processes
85 (p2): CHAPTER Ⅱ．SOME CLASSICAL THEORY
85 (p2-1): 1．BASIC MEASURE THEORY
85 (p2-1-1): Measurability and measure
85 (p2-1-1-1): 1．Measurable spaces