Probability with Martingales

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1. A branching-process example; Part I. Foundations: 2. Measure spaces; 3. Events; 4. Random variables; 5. Independence; 6. Integration; 7. Expectation; 8. An easy strong law: product measure; Part II. Martingale Theory: 9. Conditional expectation; 10. Martingales; 11. The convergence theorem; 12. Martingales bounded in L2; 13. Uniform integrability; 14. UI martingales; 15. Applications; Part III. Characteristic Functions: 16. Basic properties of CFs; 17. Weak convergence; 18. The central limit theorem; Appendices; Exercises.

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This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.

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'... one of the best introductions to Martingale theory.' Monatshefte fur Mathematik

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