- 192 pages
- English
- PDF
- Available on iOS & Android
A First Look at Rigorous Probability Theory
About This Book
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. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.
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Table of contents
- Contents
- Preface.
- 1. The need for measure theory. This introductory section is directed primarily to those
- 2. Probability triples.
- 3. Further probabilistic foundations.
- 4. Expected values.
- 5. Inequalities and laws of large numbers.
- 6. Distributions of random variables.
- 7. Stochastic processes and gambling games.
- 8. Discrete Markov chains.
- 9. Some further probability results.
- 10. Weak convergence.
- 11. Characteristic functions.
- 12. Decomposition of probability laws.
- 13. Conditional probability and expectation.
- 14. Martingales.
- 15. Introduction to other stochastic processes.
- Appendix: Mathematical Background.
- Bibliography.
- Index