Probability Theory

An Advanced Course

  • Vivek S. Borkar

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Vivek S. Borkar
    Pages 1-17
  3. Vivek S. Borkar
    Pages 19-36
  4. Vivek S. Borkar
    Pages 37-63
  5. Vivek S. Borkar
    Pages 65-87
  6. Vivek S. Borkar
    Pages 89-108
  7. Vivek S. Borkar
    Pages 109-129
  8. Back Matter
    Pages 131-139

About this book


This book presents a selection of topics from probability theory. Essentially, the topics chosen are those that are likely to be the most useful to someone planning to pursue research in the modern theory of stochastic processes. The prospective reader is assumed to have good mathematical maturity. In particular, he should have prior exposure to basic probability theory at the level of, say, K.L. Chung's 'Elementary probability theory with stochastic processes' (Springer-Verlag, 1974) and real and functional analysis at the level of Royden's 'Real analysis' (Macmillan, 1968). The first chapter is a rapid overview of the basics. Each subsequent chapter deals with a separate topic in detail. There is clearly some selection involved and therefore many omissions, but that cannot be helped in a book of this size. The style is deliberately terse to enforce active learning. Thus several tidbits of deduction are left to the reader as labelled exercises in the main text of each chapter. In addition, there are supplementary exercises at the end. In the preface to his classic text on probability ('Probability', Addison­ Wesley, 1968), Leo Breiman speaks of the right and left hands of probability.


Markov chain Markov property Martingale Operations Research Probability theory Random variable Stochastic processes Uniform integrability stochastic process

Authors and affiliations

  • Vivek S. Borkar
    • 1
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94558-3
  • Online ISBN 978-1-4612-0791-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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