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...
| Autores principales: | , |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York
2007.
|
| Edición: | 1st ed. 2007. |
| Colección: | Universitext,
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009462232406719 |
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.
