An Intermediate Course in Probability

  • Authors
  • AllanĀ Gut

Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages 1-27
  2. Allan Gut
    Pages 15-29
  3. Allan Gut
    Pages 31-55
  4. Allan Gut
    Pages 57-99
  5. Allan Gut
    Pages 101-116
  6. Allan Gut
    Pages 117-145
  7. Allan Gut
    Pages 147-185
  8. Allan Gut
    Pages 187-220
  9. Allan Gut
    Pages 221-275
  10. Back Matter
    Pages 1-26

About this book

Introduction

The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theory before entering into more advanced courses. The first six chapters focus on some central areas of what might be called pure probability theory: multivariate random variables, conditioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process as a means both to introduce stochastic processes and to apply many of the techniques introduced earlier in the text.

Students are assumed to have taken a first course in probability, though no knowledge of measure theory is assumed. Throughout, the presentation is thorough and includes many examples that are discussed in detail. Thus, students considering more advanced research in probability theory will benefit from this wide-ranging survey of the subject that provides them with a foretaste of the subject's many treasures.

The present second edition offers updated content, one hundred additional problems for solution, and a new chapter that provides an outlook on further areas and topics, such as stable distributions and domains of attraction, extreme value theory and records, and martingales. The main idea is that this chapter may serve as an appetizer to the more advanced theory.

Allan Gut is Professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is a member of the International Statistical Institute, the Bernoulli Society, the Institute of Mathematical Statistics, and the Swedish Statistical Society. He is an Associate Editor of the Journal of Statistical Planning and Inference and Sequential Analysis, a former Associate Editor of the Scandinavian Journal of Statistics, and the author of five other books including Probability: A Graduate Course (Springer, 2005) and Stopped Random Walks: Limit Theorems and Applications, Second Edition (Springer, 2009).

Keywords

Martingale Measure Normal distribution Poisson process Probability theory Random variable statistics stochastic process

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-0162-0
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-0161-3
  • Online ISBN 978-1-4419-0162-0
  • Series Print ISSN 1431-875X
  • About this book