Image from Coce

Probability essentials / Jean Jacod, Philip Protter.

By: Contributor(s): Material type: TextTextSeries: UniversitextPublisher: Berlin ; New York : Springer, [2003]Copyright date: ©2003Edition: Second editionDescription: x, 254 pages : illustrations ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 3540438718
  • 9783540438717
Subject(s): DDC classification:
  • 519.2 21
LOC classification:
  • QA273 .J26 2003
Contents:
1. Introduction -- 2. Axioms of Probability -- 3. Conditional Probability and Independence -- 4. Probabilities on a Finite or 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 R[superscript n] -- 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. L[superscript 2] and Hilbert Spaces -- 23. Conditional Expectation -- 24. Martingales -- 25. Supermartingales and Submartingales -- 26. Martingale Inequalities -- 27. Martingale Convergence Theorems -- 28. The Randon-Nikodym Theorem.
Review: "This introduction to probability theory 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 (economics), electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of martingale theory. After learning probability theory from this text, 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."--BOOK JACKET.
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references (pages 249-250) and index.

1. Introduction -- 2. Axioms of Probability -- 3. Conditional Probability and Independence -- 4. Probabilities on a Finite or 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 R[superscript n] -- 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. L[superscript 2] and Hilbert Spaces -- 23. Conditional Expectation -- 24. Martingales -- 25. Supermartingales and Submartingales -- 26. Martingale Inequalities -- 27. Martingale Convergence Theorems -- 28. The Randon-Nikodym Theorem.

"This introduction to probability theory 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 (economics), electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of martingale theory. After learning probability theory from this text, 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."--BOOK JACKET.

Machine converted from AACR2 source record.

There are no comments on this title.

to post a comment.

Powered by Koha