Probability Essentials

  • Jean Jacod
  • Philip Protter

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Jean Jacod, Philip Protter
    Pages 1-3
  3. Jean Jacod, Philip Protter
    Pages 5-10
  4. Jean Jacod, Philip Protter
    Pages 11-16
  5. Jean Jacod, Philip Protter
    Pages 17-19
  6. Jean Jacod, Philip Protter
    Pages 21-29
  7. Jean Jacod, Philip Protter
    Pages 31-33
  8. Jean Jacod, Philip Protter
    Pages 35-42
  9. Jean Jacod, Philip Protter
    Pages 43-46
  10. Jean Jacod, Philip Protter
    Pages 47-60
  11. Jean Jacod, Philip Protter
    Pages 61-72
  12. Jean Jacod, Philip Protter
    Pages 73-81
  13. Jean Jacod, Philip Protter
    Pages 83-97
  14. Jean Jacod, Philip Protter
    Pages 99-105
  15. Jean Jacod, Philip Protter
    Pages 107-112
  16. Jean Jacod, Philip Protter
    Pages 113-119
  17. Jean Jacod, Philip Protter
    Pages 137-145
  18. Jean Jacod, Philip Protter
    Pages 147-162
  19. Jean Jacod, Philip Protter
    Pages 163-167

About this book

Introduction

We present here a one-semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to fill a current need: there are mathematically sophisticated stu­ dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Prob­ ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it difficult to construct a lean one semester course that covers (what we believe are) the essential topics. Chapters 1-23 provide such a course. We have indulged ourselves a bit by including Chapters 24-28 which are highly optional, but which may prove useful to Economists and Electrical Engineers. This book had its origins in a course the second author gave in Perugia, Italy, in 1997; he used the samizdat "notes" of the first author, long used for courses at the University of Paris VI, augmenting them as needed. The result has been further tested at courses given at Purdue University. We thank the indulgence and patience of the students both in Perugia and in West Lafayette. We also thank our editor Catriona Byrne, as weil as Nick Bingham for many superb suggestions, an anonymaus referee for the same, and Judy Mitchell for her extraordinary typing skills. Jean Jacod, Paris Philip Protter, West Lafayette Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . .

Keywords

Brownian motion Martingal Martingale Martingales Random variable central limit theorem conditional probability convergence of random variables measure theory normal distribution probability probability distribution probability measure probability theory

Authors and affiliations

  • Jean Jacod
    • 1
  • Philip Protter
    • 2
  1. 1.Laboratoire de ProbabilitésUniversité de Paris VIParis Cedex 05France
  2. 2.Mathematics and Statistics DepartmentsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-51431-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66419-2
  • Online ISBN 978-3-642-51431-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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