Probability with martingales
 Author/Creator
 Williams, D. (David), 1938
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, c1991.
 Physical description
 xv, 251 p. ; 23 cm.
 Series
 Cambridge mathematical textbooks
Access
Available online
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 243245).
 Contents

 1. A branchingprocess 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the ThreeSeries Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature 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; and it assumes certain key results from measure theory in the main text. These measuretheoretic results are proved in full in appendices, so that the book is completely selfcontained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital role. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.
(source: Nielsen Book Data)
Subjects
 Subject
 Martingales (Mathematics)
Bibliographic information
 Publication date
 1991
 Responsibility
 David Williams.
 Note
 Includes index.
 ISBN
 052140455X
 0521406056
 9780521404556
 9780521406055