Probability essentials = 概率论基础
发布日期:2011-06-02 浏览次
[内容简介]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．
[目次]1 Introduction
2 Axioms of Probability
3 Conditional Probability and Independence
4 Probabilities on a Finite or Countable Space
5 Random Variables on a Countable Space
6 Construction of a Probability Measure
7 Construction of a Probability Measure on R
8 Random Variables
9 Integration with Respect to a Probability Measure
10 Independent Random Variables
11 Probability Distributions on R
12 Probability Distributions on R”
13 Characteristic Functions
14 Properties of Characteristic Functions
15 Sums of Independent Random Variables
16 Gaussian Random Variables(The Normal and the Multivariate Normal Distributions)
17 Convergence of Random Variables
18 Weak Convergence
19 Weak Convergence and Characteristic Functions
20 The Laws of Large Numbers
20 The Laws of Large Numbers
21 The Central Limit Theorem
22 L2 and Hilbert Spaces
23 Conditional Expectation
24 Martingales
25 Supermartingales and Submartingales
26 Martingale Inequalities
27 Martingale Convergence Theorems
28 The Radon-Nikodym Theorem
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