A Basic Course in Probability Theory (Paperback)

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.