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© 1997

A Modern Approach to Probability Theory

Textbook

Part of the Probability and its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Probability Spaces, Random Variables, and Expectations

    1. Front Matter
      Pages 1-2
    2. Bert Fristedt, Lawrence Gray
      Pages 3-10
    3. Bert Fristedt, Lawrence Gray
      Pages 11-24
    4. Bert Fristedt, Lawrence Gray
      Pages 25-40
    5. Bert Fristedt, Lawrence Gray
      Pages 41-58
    6. Bert Fristedt, Lawrence Gray
      Pages 59-74
    7. Bert Fristedt, Lawrence Gray
      Pages 75-84
    8. Bert Fristedt, Lawrence Gray
      Pages 85-100
    9. Bert Fristedt, Lawrence Gray
      Pages 101-118
  3. Independence and Sums

    1. Front Matter
      Pages 119-120
    2. Bert Fristedt, Lawrence Gray
      Pages 121-146
    3. Bert Fristedt, Lawrence Gray
      Pages 147-162
    4. Bert Fristedt, Lawrence Gray
      Pages 163-184
    5. Bert Fristedt, Lawrence Gray
      Pages 185-208
    6. Bert Fristedt, Lawrence Gray
      Pages 209-240
  4. Convergence in Distribution

    1. Front Matter
      Pages 241-242
    2. Bert Fristedt, Lawrence Gray
      Pages 243-270
    3. Bert Fristedt, Lawrence Gray
      Pages 271-288
    4. Bert Fristedt, Lawrence Gray
      Pages 289-322

About this book

Introduction

Overview This book is intended as a textbook in probability for graduate students in math­ ematics and related areas such as statistics, economics, physics, and operations research. Probability theory is a 'difficult' but productive marriage of mathemat­ ical abstraction and everyday intuition, and we have attempted to exhibit this fact. Thus we may appear at times to be obsessively careful in our presentation of the material, but our experience has shown that many students find them­ selves quite handicapped because they have never properly come to grips with the subtleties of the definitions and mathematical structures that form the foun­ dation of the field. Also, students may find many of the examples and problems to be computationally challenging, but it is our belief that one of the fascinat­ ing aspects of prob ability theory is its ability to say something concrete about the world around us, and we have done our best to coax the student into doing explicit calculations, often in the context of apparently elementary models. The practical applications of probability theory to various scientific fields are far-reaching, and a specialized treatment would be required to do justice to the interrelations between prob ability and any one of these areas. However, to give the reader a taste of the possibilities, we have included some examples, particularly from the field of statistics, such as order statistics, Dirichlet distri­ butions, and minimum variance unbiased estimation.

Keywords

Algebra Finite Probability space Probability theory Random variable Sage Variable Variance bayesian statistics calculus function mathematics measure theory theorem

Authors and affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • Book Title A Modern Approach to Probability Theory
  • Authors Bert E. Fristedt
    Lawrence F. Gray
  • Series Title Probability and its Applications
  • DOI https://doi.org/10.1007/978-1-4899-2837-5
  • Copyright Information Birkhäuser Boston 1997
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3807-8
  • Softcover ISBN 978-1-4899-2839-9
  • eBook ISBN 978-1-4899-2837-5
  • Edition Number 1
  • Number of Pages XX, 758
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site

Reviews

"Covers the essentials in a clear and readable fashion… A must for professionals and an attractive text for a graduate course."   —American Mathematical Monthly  (review of the first edition)

"This ambitious book is intended as ‘a textbook in probability for graduate students in mathematics and related areas such as economics, statistics, physics and operations research’…The coverage is careful and thorough…Quite a lot of fairly recent material is incorporated, and this is certainly one of the book’s strengths. The selection of material is sensible, and the quality of exposition is good…In sum: the book contains a lot of good mathematics, nicely done, and should prove useful to students and teachers, and to specialists in probability theory."   —Mathematical Reviews (review of the first edition)

"The book takes the reader from a relatively low level.... To the point where he or she can specialize in research topics of current interest. ...an outstanding basis for teaching a graduate course in probability theory. The exhaustive compilation of results and detailed index also make it a very useful reference text for the more advanced probabilist... a good buy for anyone looking for a very accessible and complete mathematical account of modern probability theory."   —Journal of the American Statistical Association  (review of the first edition)