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A first look at rigorous probability theory / Jeffrey S. Rosenthal.

By: Material type: TextTextPublisher: Hackensack, N.J. : World Scientific, 2006Copyright date: ©2006Edition: Second editionDescription: xvi, 219 pages : illustrations ; 23 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9812703713 (pbk)
  • 9789812703712 (pbk)
  • 9812703705
  • 9789812703705
Subject(s): DDC classification:
  • 519.2 23
LOC classification:
  • QA273 .R67 2006
Contents:
The need for measure theory -- Probability triples -- Further probabilistic foundations -- Expected values -- Inequalities and convergence -- Distributions of random variables -- Stochastic processes and gambling games -- Discrete Markov chains -- More probability theorems -- Weak convergence -- Characteristic functions -- Decomposition of probability laws -- Conditional probability and expectation -- Martingales -- General stochastic processes -- Mathematical background.
1. The need for measure theory -- 2. Probability triples -- 3. Further probabilistic foundations -- 4. Expected values -- 5. Inequalities and convergence -- 6. Distributions of random variables -- 7. Stochastic processes and gambling games -- 8. Discrete Markov chains -- 9. More probability theorems -- 10. Weak convergence -- 11. Characteristic functions -- 12. Decomposition of probability laws -- 13. Conditional probability and expectation -- 14. Martingales -- 15. General stochastic processes.
Review: "This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results."--BOOK JACKET.
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Holdings
Item type Current library Call number Copy number Status Date due Barcode
Book City Campus City Campus Main Collection 519.2 ROS (Browse shelf(Opens below)) 1 Available A547647B

Includes bibliographical references (pages 209-211) and index.

The need for measure theory -- Probability triples -- Further probabilistic foundations -- Expected values -- Inequalities and convergence -- Distributions of random variables -- Stochastic processes and gambling games -- Discrete Markov chains -- More probability theorems -- Weak convergence -- Characteristic functions -- Decomposition of probability laws -- Conditional probability and expectation -- Martingales -- General stochastic processes -- Mathematical background.

1. The need for measure theory -- 2. Probability triples -- 3. Further probabilistic foundations -- 4. Expected values -- 5. Inequalities and convergence -- 6. Distributions of random variables -- 7. Stochastic processes and gambling games -- 8. Discrete Markov chains -- 9. More probability theorems -- 10. Weak convergence -- 11. Characteristic functions -- 12. Decomposition of probability laws -- 13. Conditional probability and expectation -- 14. Martingales -- 15. General stochastic processes.

"This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results."--BOOK JACKET.

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