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A Basic Course in Probability Theory
The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively ea...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2007.
|
| Edición: | 1st ed. 2007. |
| Colección: | Universitext,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- Random Maps, Distribution, and Mathematical Expectation
- Independence, Conditional Expectation
- Martingales and Stopping Times
- Classical Zero-One Laws, Laws of Large Numbers and Deviations
- Weak Convergence of Probability Measures
- Fourier Series, Fourier Transform, and Characteristic Functions
- Classical Central Limit Theorems
- Laplace Transforms and Tauberian Theorem
- Random Series of Independent Summands
- Kolmogorov's Extension Theorem and Brownian Motion
- Brownian Motion: The LIL and Some Fine-Scale Properties
- Skorokhod Embedding and Donsker's Invariance Principle
- A Historical Note on Brownian Motion.