扩散 马尔可夫过程和鞅 第1卷
2003-1
世界图书出版公司
L.C.G.Rogers,D.Williams著
386
无
Long ago （or so it seems today）, Chung wrote on page 196 of his book [1]:'One wonders if the present theory of stochastic processes is not still too difficult for applications.' Advances in the theory since that time have been phenomenal,but these have been accompanied by an increase in the technical difficulty of the subject so bewildering as to give a quaint charm to Chung's use of the word 'still'. Meyer writes in the preface to his definitive account of stochastic integral theory: '... il faut. . . un cours de six mois sur les definitions. Que peut on y faire?' I have thought up as intuitive a picture of the subject as I can, written it down at speed, and refused to be lured back by piety （or even by wit!） to cancel half a line. 'First' intuition, which is what you need when you are learning the subject, is raw, rough and ready; and, as you have guessed, I make the excuse that it demands a compatible style and lack of polish. Note that I wrote 'first intuition'. Consider an example. Meyer's concept of a right process is exactly right for Markov process theory, but the concept is the result of a long evolution. To understand it properly, you need a highly developed intuition, and that takes time to acquire. The difficulty with the best advanced literature is that its authors have too much intuition; never make the mistake of thinking otherwise.
Some Frequently Used NotationCHAPTERⅠ. BROWNIAN MOTION1. INTRODUCTION 1. What is Brownian motion, and why study it 2. Brownian motion as a martingale 3. Brownian motion as a Gaussian process 4. Brownian motion as a Markov process 5. Brownian motion as a diffusion and martingale2. BASICS ABOUT BROWNIAN MOTION 6. Existence and uniqueness of Brownian motion 7. Skorokhod embedding 8. Donsker''s Invariance Principle 9. Exponential martingales and first-passage distributions 10. Some sample-path properties 11. Quadratic variation 12. The strong Markov property 13. Reflection 14. Reflecting Brownian motion and local time 15. Kolmogorov''s test 16. Brownian exponential martingales and the Law of the Iterated Logarithm3. BROWNIAN MOTION IN HIGHER DIMENSIONS 17. Some martingales for Brownian motion 18. Recurrence and transience in higher dimensions 19. Some applications of Brownian motion to complex analysis 20. Windings of planar Brownian motion 21. Multiple points, cone points, cut points 22. Potential theory of Brownian motion in Rd d ≥ 3 23. Brownian motion and physical diffusion4. GAUSSIAN PROCESSES AND LEVY PROCESSES Gaussian processes 24. Existence results for Gaussian processes 25. Continuity results 26. Isotropic random flows 27. Dynkin''s Isomorphism Theorem Levy processes 28. Levy processes 29. Fluctuation theory and Wiener-Hopf factorisation 30. Local time of Levy processesCHAPTERⅡ. SOME CLASSICAL THEORY 1. BASIC MEASURE THEORY Measurability and measure 1. Measurable spaces; a-algebras; n-systems; d-systems 2. Measurable functions 3. Monotone-Class Theorems 4. Measures; the uniqueness lemma; almost everywhere; a.e. u,∑ 5. Caratheodory''s Extension Theorem 6. Inner and outer u-measures; completion Integration 7. Definition of the integral f du 8. Convergence theorems 9. The Radon-Nikodym Theorem; absolute continuity;
无
推荐阅读
看完再说，书果断买了
好书，内容深入
Rogers的这两本书总体写的挺不错的，Rogers也是相当令我崇拜的教授，但第一章偏难了不太方便新手入门建议可以从第二章开始看
全面 细致 有深度 适合全面系统的学习随机分析 看完此书后可以看 布朗运动和随机计算。
还没看，第2本是教材，顺便把这本也买了
是不是盗版。不过书的内容合理，难度适中。