A first look at rigorous probability theory

By: Jeffery S. RosenthalPublication details: Singapore: World Scientific Publishing Co. Pte. Ltd. [c2006]Edition: 2nd EdDescription: 219 pISBN: 9789812703712Subject(s): MathematicsLOC classification: QA273. R784
Contents:
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
Summary: 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. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. --- summary provided by publisher
List(s) this item appears in: New Arrivals
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Item type Current library Collection Shelving location Call number Status Date due Barcode Item holds
Book Book ICTS
Mathematics Rack No 5 QA273 .R784 (Browse shelf (Opens below)) Checked out to Arup Datta (0008448394) 12/27/2024 02858
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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. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. --- summary provided by publisher

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