A Basic Course in Probability Theory

  • Rabi Bhattacharya
  • Edward C. Waymire

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Rabi Bhattacharya, Edward C. Waymire
    Pages 1-23
  3. Rabi Bhattacharya, Edward C. Waymire
    Pages 25-52
  4. Rabi Bhattacharya, Edward C. Waymire
    Pages 53-74
  5. Rabi Bhattacharya, Edward C. Waymire
    Pages 75-85
  6. Rabi Bhattacharya, Edward C. Waymire
    Pages 87-102
  7. Rabi Bhattacharya, Edward C. Waymire
    Pages 103-134
  8. Rabi Bhattacharya, Edward C. Waymire
    Pages 135-157
  9. Rabi Bhattacharya, Edward C. Waymire
    Pages 159-166
  10. Rabi Bhattacharya, Edward C. Waymire
    Pages 167-178
  11. Rabi Bhattacharya, Edward C. Waymire
    Pages 179-186
  12. Rabi Bhattacharya, Edward C. Waymire
    Pages 207-210
  13. Back Matter
    Pages 225-265

About this book

Introduction

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.  General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of  Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem.

The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference.

Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

Keywords

Probability Martingales Zero-one laws Brownian motion Markov processes Weak convergence Conditional expectation Conditional probability

Authors and affiliations

  • Rabi Bhattacharya
    • 1
  • Edward C. Waymire
    • 2
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of MathematicsOregon State Univeristy Department of MathematicsCorvallisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-47974-3
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-47972-9
  • Online ISBN 978-3-319-47974-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book