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A graduate course in probability /
A Graduate Course in Probability.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1967.
|
| Colección: | Probability and mathematical statistics ;
2. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; A Graduate Course in Probability; Copyright Page; Dedication; Preface; Table of Contents; CHAPTER 1. Probability Spaces; 1.1 Sigma Fields; 1.2 Probability Measures; 1.3 Random Variables; CHAPTER 2. Probability Distributions; 2.1. Univariate Distribution Functions; 2.2. Multivariate Distribution Functions; 2.3. Distribution of a Set of Infinitely Many Random Variables; 2.4. Expectation; 2.5. Characteristic Functions; CHAPTER 3. Stochastic Independence; 3.1. Independent Events; 3.2. Independent Random Variables; 3.3. The Zero-One Law; CHAPTER 4. Basic Limiting Operations.
- 4.1. Convergence of Distribution Functions4.2. The Continuity Theorem; 4.3. Refinements of the Continuity Theorem for Nonvanishing Characteristic Functions; 4.4. The Four Types of Convergence: Almost Sure, in Law, in Probability, and in rth Mean; CHAPTER 5. Strong Limit Theorems for Independent Random Variables; 5.1. Almost Sure Convergence of Series of Independent Random Variables; 5.2. Proof that Convergence in Law of a Series of Independent Random Variables Implies Almost Sure Convergence; 5.3. The Strong Law of Large Numbers; 5.4. The Glivenko-Cantelli Theorem.
- 5.5. Inequalities for the Law of the Iterated Logarithm5.6. The Law of the Iterated Logarithm; CHAPTER 6. The Central Limit Theorem; 6.1. Infinitely Divisible Distributions; 6.2. Canonical Representation of Infinitely Divisible Characteristic Functions; 6.3 Convergence of Infinitely Divisible Distribution Functions; 6.4. Infinitesimal Systems of Random Variables; 6.5. The General Limit Theorem for Sequences of Sums of Independent Random Variables; 6.6. Convergence to the Normal and Poisson Distributions; CHAPTER 7. Conditional Expectation and Martingale Theory; 7.1. Conditional Expectation.
- 7.2. Martingales and Submartingales7.3. Martingale and Submartingale Convergence Theorems; 7.4. Brownian Motion; CHAPTER 8. An Introduction to Stochastic Processes and, in Particular, Brownian Motion; 8.1 Probability Measures over Function Spaces; 8.2 Separable Stochastic Processes; 8.3 Continuity and Nonrectifiability of Almost All Sample Functions of Separable Brownian Motion; 8.4. The Law of the Iterated Logarithm for Separable Brownian Motion; Suggested Reading; Index.