Probability Theory with Applications

  • M. M. Rao
  • R. J. Swift

Part of the Mathematics and Its Applications book series (MAIA, volume 582)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Foundations

  3. Analytical Theory

    1. Front Matter
      Pages 221-221
    2. Pages 291-408
  4. Applications

  5. Back Matter
    Pages 509-527

About this book


Probability Theory and Applications is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include:

 • indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems;

 • attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject;

 • providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks.

Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.


This book is intended for graduate students and researchers interested in probability theory.


Characteristic functions Convergence of random series Distribution Markov dependence Probability distribution Probability theory Random Fourier series Weak limit laws

Authors and affiliations

  • M. M. Rao
    • 1
  • R. J. Swift
    • 2
  1. 1.University of CaliforniaRiverside
  2. 2.California State Polytechnic UniversityPomona

Bibliographic information

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