
Probability with Martingales
David Williams(Autor*in)
Cambridge University Press
Erschienen am 14. Februar 1991
Buch
Softcover
265 Seiten
978-0-521-40605-5 (ISBN)
Beschreibung
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 Three-Series 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 measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. 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.
Rezensionen / Stimmen
'... one of the best introductions to Martingale theory.' Monatshefte fuer MathematikWeitere Details
Sprache
Englisch
Verlagsort
Cambridge
Großbritannien
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Broschur/Paperback
Illustrationen
3 Line drawings, unspecified
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 15 mm
Gewicht
393 gr
ISBN-13
978-0-521-40605-5 (9780521406055)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Weitere Ausgaben
Andere Ausgaben

David Williams
Probability with Martingales
E-Book
07/2013
1. Auflage
Cambridge University Press
42,49 €
Als Download verfügbar

David Williams
Probability with Martingales
Buch
02/1991
Cambridge University Press
40,13 €
Artikel ist vergriffen; siehe Neuauflage

David Williams
Probability with Martingales
E-Book
02/1991
Cambridge University Press
35,49 €
Als Download verfügbar
Vorauflage

David Williams
Probability with Martingales
Buch
02/1991
Cambridge University Press
40,13 €
Artikel ist vergriffen; siehe Neuauflage
Person
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.
Inhalt
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.