概率论基础

1 Introduction2 Axioms of Probability3 Conditional Probability and Independence4　Probabilities on a Finite or Countable Space5 Random Variables on a Countable Space6 Construction of a Probability Measure7 Construction of a Probability Measure on R8 Random Variables9 Integration with Respect to a Probability Measure10 Independent Random Variables11 Probability Distributions on R12 Probability Distributions on R”13 Characteristic Functions14 Properties of Characteristic Functions15 Sums of Independent Random Variables

1 Introduction2 Axioms of Probability3 Conditional Probability and Independence4　Probabilities on a Finite or Countable Space5 Random Variables on a Countable Space6 Construction of a Probability Measure7 Construction of a Probability Measure on R8 Random Variables9 Integration with Respect to a Probability Measure10 Independent Random Variables11 Probability Distributions on R12 Probability Distributions on R”13 Characteristic Functions14 Properties of Characteristic Functions15 Sums of Independent Random Variables16 Gaussian Random Variables(The Normal and the Multivariate Normal Distributions)17 Convergence of Random Variables18 Weak Convergence19 Weak Convergence and Characteristic Functions20 The Laws of Large Numbers……ReferencesIndex

This introduction to Probability Theory can be used，at the beginning graduate level．for a one—semester course on Probability Theory or for self-direction without benefit of a formal course：the measure theory needed iS developed in the text．It will also be useful for students and teachers in related areaS such as Finance Theory (Economics)，Electrical Engineerin9，and Operations Research．The text covers the essentials in a directed and lean way with 28 short chapters．Assuming of readers only an undergraduate background in mathematics，it brings them from a starting knowledge ofthe subject to a knowledge ofthe basics ofMartingale Theory．Afler learning Probability Theory foFin this text，the interested student will be ready to continue with the study of more advanced topics，such as Brownian Motion andIto Calculus．or Statistical Inference．The second edition contains some additionsto the text and to the references and some parts are completely rewritten．