Bibliographic Information

Probability essentials

Jean Jacod, Philip Protter

(Universitext)

Springer, 2004

2nd ed., corr. 2nd printing

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Note

Includes bibliographical references (p. [249]-250) and index

Description and Table of Contents

Description

This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.

Table of Contents

1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on Rn 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingales Convergence Theorems 28. The Radon-Nikodym Theorem

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Details

  • NCID
    BB0603757X
  • ISBN
    • 9783540438717
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin ; Tokyo
  • Pages/Volumes
    x, 254 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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