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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2007, 2007
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| Edition: | 1st ed. 2007 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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