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A basic course in probability theory / Rabi Bhattacharya, Edward C. Waymire.

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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....

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Authors: Bhattacharya, R. N. (Rabindra Nath), 1937- (Author), Waymire, Edward C. (Author)
Format: eBook
Language:English
Published: Cham, Switzerland : Springer, 2016.
Edition:Second edition.
Series:Universitext.
Subjects:
Probabilities.
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.

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