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A Probability Path

  • Sidney I. Resnick

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sidney I. Resnick
    Pages 1-27
  3. Sidney I. Resnick
    Pages 29-70
  4. Sidney I. Resnick
    Pages 71-90
  5. Sidney I. Resnick
    Pages 91-116
  6. Sidney I. Resnick
    Pages 117-166
  7. Sidney I. Resnick
    Pages 167-201
  8. Sidney I. Resnick
    Pages 247-291
  9. Sidney I. Resnick
    Pages 333-441
  10. Back Matter
    Pages 443-453

About this book

Introduction

​​Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.

 

A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation), and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance.

 

Like Adventures in Stochastic Processes, Resnick’s related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience. 

                                                          

This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance.... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems.

—Publications of the International Statistical Institute    

 

This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics.... Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications.

—Revue Roumaine de Mathématiques Pures et Appliquées

Keywords

central limit theorem expectation independence martingales measure theory

Authors and affiliations

  • Sidney I. Resnick
    • 1
  1. 1.Cornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8409-9
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8408-2
  • Online ISBN 978-0-8176-8409-9
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • Buy this book on publisher's site
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