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出版社:世界圖書出版公司
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ISBN:7506259214
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作者:L.C.G.Rogers//D.Williams
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頁數:386
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出版日期:2003-01-01
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印刷日期:2003-01-01
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包裝:平裝
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開本:24開
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版次:1
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印次:1
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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...
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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 IRd(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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