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Probability with Martingales

Author: David Williams
Publisher: Cambridge : Cambridge University Press, ©1991.
Series: Cambridge mathematical textbooks.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Document Type: Book
All Authors / Contributors: David Williams
ISBN: 052140455X 9780521404556 0521406056 9780521406055
OCLC Number: 318331344
Description: xv, 251 p. : il. ; 24 cm.
Contents: 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.
Series Title: Cambridge mathematical textbooks.
Responsibility: David Williams.

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'... one of the best introductions to Martingale theory.' Monatshefte fur Mathematik "Williams, who writes as though he were reading the reader's mind, does a brilliant job of leaving it all in. Read more...

 
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