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扩散 马尔可夫过程和鞅 第1卷

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扩散 马尔可夫过程和鞅 第1卷

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定 价：￥63.00

作 者：L.C.G.Rogers,D.Williams 著 著

出 版 社：世界图书出版公司

出版时间：2003-1-1

I S B N：9787506259217

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    内容简介
    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.

    作者简介

    目录
    Some Frequently Used Notation
    CHAPTERⅠ. BROWNIAN MOTION
    1. 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 martingale
    2. 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 Logarithm
    3. 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 diffusion
    4. 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 processes
    CHAPTERⅡ. 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;<< notation; equivalent measures
    　　　10. Inequalities; and spaces p ≥ 1
    　　Product structures
    　　　11. Product a-algebras
    　　　12. Product measure; Fubini''s Theorem
    　　　13. Exercises
    　2. BASIC PROBABILITY THEORY
    　　Probability and expectation
    　　　14. Probability triple; almost surely a.s. ; a.s. P , a.s. P,F
    　　　15. lim sup En: First Borel-Cantelli Lemma
    　　　16. Law of random variable; distribution function: joint law
    　　　17. Expectation: E X; F
    　　　18. Inequalities: Markov, Jensen, Schwarz, Tchebychev
    　　　19. Modes of convergence of random variables
    　　Uniform integrability and L1 convergence
    　　　20. Uniform integrability
    　　　21. L1 convergence
    　　Independence
    　　　22. Independence of a-algebras and of random variables
    　　　23. Existence of families of independent variables
    　　　24. Exercises
    3. STOCHASTIC PROCESSES
    4. DISCRETE-PARAMETER MARTINGALE THEORY
    5. CONTINUOUS-PARAMETER SUPERMARTINGALES
    CHAPTERⅢ.MARKOV PROCESSES
    1. TRANSITION FUNCTIONS AND RESOLVENTS
    2. FELLER-DYNKIN PROCESSES
    3. ADDITIVE FUNCTIONALS
    4. APPROACH TO RAY PROCESSES:
    5. RAY PROCESSES
    6. APPLICATIONS
    References for Volumes 1 and 2
    Index to Volumes 1 and 2

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