概率和随机

PrefaceFrequently Used NotationⅠ Measure and Integration1 Measurable Spaces2 Measurable Functions3 Measures4 Integration5 Transforms and Indefinite Integrals6 Kernels and Product SpacesⅡ Probability Spaces1 Probability Spaces and Random Variables2 Expectations3 LP—spaces and Uniform Integrability4 Information and Determinability5 IndependenceⅢ Convergence1 Convergence of Real Sequences2 Almost Sure Convergence3 Convergence in Probability4 Convergencein Lp5 Weak Convergence6 Laws ofLarge Numbers7 Convergence ofSeries8 CentraILimitsⅣ Conditioning1 Conditional Expectations2 Conditional Probabilities and Distributions3 Conditionallndependence4 Construction of Probability Spaces5 Special ConstructionsⅤ Martingales and Stochastics1 Filtrations and Stopping Times2 Martingales3 Martingale Transformations and Maxima4 Martingale Convergence5 Martingales in Continuous Time6 Martingale Characterizations for Wiener and Poisson7 Standard Filtrations and Modifications of MartingalesⅥ Poisson Random Measures1 Random Measures2 Poisson Random Measures3 Transformations4 Additive Random Measures and Levy Processes5 Poisson Processes6 Poisson Integrals and Self—exciting ProcessesⅦ Levy Processes1 Introduction2 Stable Processes3 Levy Processes on Standard Settings4 Characterizations for Wiener and Poisson5 Ito—Levy Decomposition6 Subordination7 Increasing Levy ProcessesⅧ Brownian Motion1 Introduction2 Hitting Times and Recurrence Times3 Hitting Times and Running Maximum4 Wiener and its Maximum5 Zeros，LocaITimes6 Excursions7 Path Properties8 ExistenceⅨ Markov Processes1 Markov Property2 Ito Diffusions3 Jump—Diffusions4 Markov Systems5 Hunt Processes6 Potentials and Excessive Functions7 Appendix：Stochastic IntegrationNotes and CommentsBibliographyIndex

This is an introduction to the modern theory of probability and stochastic processes. The aim is to enable the student to have access to the many excellent research monographs in the literature. It might be regarded as an updated version of the textbooks by Breiman， Chung， and Neveu， just to name three.　　The book is based on the lecture notes for a two-semester course which I have offered for many years. The course is fairly popular and attracts grad uate students in engineering， economics， physics， and mathematics， and a few overachieving undergraduates. Most of the students had familiarity with elementary probability， but it was safer to introduce each concept carefully and in a uniform style，　　As Martin Barlow put it once， mathematics attracts us because the need to memorize is minimal. So， only the more fundamental facts are labeled as theorems； they are worth memorizing. Most other results are put as propo- sitions， comments， or exercises Also put as exercises are results that can be understood only by doing the tedious work necessary. I believe in the Chinese proverb： I hear， I forget； I see， I remember； I do， I know.　　I have been considerate： I do not assume that the reader will go through the book line by line from the beginning to the end. Some things are re called or re-introduced when they are needed. In each chapter or section， the essential material is put first， technical material is put toward the end. Sub-hea-dings are used to introduce the subjects and results； the reader should　　have a quick overview by flipping the pages and reading the headings.　　The style and coverage is geared toward.the theory of stochastic processes， but with some attention to the applications. The reader will find many in- stances where the gist of the problem is introduced in practical， everyday language， and then is made precise in mathematical form. Conversely， many a theoretical point is re-stated in heuristic terms in order to develop the intuition and to provide some experience in stochastic modeling.