A Basic Course in Probability Theory

• Main Authors: Bhattacharya, Rabi (Author), Waymire, Edward C. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Series: Universitext
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Probabilities.; Probability Theory and Stochastic Processes.; Measure and Integration.; Analysis.

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...

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.