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: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Edition: 2nd ed. 2016.
• Series: Universitext,
• Subjects: Mathematics.; Measure theory.; Probabilities.; Probability Theory and Stochastic Processes.; Measure and Integration.

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded....

Table of Contents:

• Preface to Second Edition
• Preface to First Edition
• I. Random Maps, Distribution, and Mathematical Expectation
• II. Independence, Conditional Expectation
• III. Martingales and Stopping Times
• IV. Classical Central Limit Theorems
• V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations
• VI. Fourier Series, Fourier Transform, and Characteristic Functions
• VII. Weak Convergence of Probability Measures on Metric Spaces
• VIII. Random Series of Independent Summands
• IX. Kolmogorov's Extension Theorem and Brownian Motion
• X. Brownian Motion: The LIL and Some Fine-Scale Properties
• XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle
• XII. A Historical Note on Brownian Motion
• XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium
• A. Measure and Integration
• B. Topology and Function Spaces
• C. Hilbert Spaces and Applications in Measure Theory
• References
• Symbol Index
• Subject Index.