This key book is a rigorous account which has Doob's theory of martingales in discrete time as its main theme. A distinguishing feature of this study is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals.
This key book is a rigorous account which has Doob's theory of martingales in discrete time as its main theme. A distinguishing feature of this study is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals.
Disclaimer. We have made every effort to make certain that all information is factually correct, comprehensive, and up-to-date. However, this book should not be used as a substitute for the knowledge and expertise of a licensed healthcare professional. You should always consult your doctor or other healthcare professionals before taking any medication. The drug information contained herein is subject to change and is not intended to cover all possible uses, directions, precautions, warnings, drug interactions, allergic reactions, or adverse effects. The absence of warnings or other information for a given drug does not indicate that the drug or drug combination is safe, effective, or appropriate for all patients or all specific uses.
Inhaltsangabe
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.
