Continuous Martingales and Brownian Motion
(Sprache: Englisch)
3rd edition: proofs have been streamlined, errors removed, new exercises added and the bibliography enlarged
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Produktinformationen zu „Continuous Martingales and Brownian Motion “
3rd edition: proofs have been streamlined, errors removed, new exercises added and the bibliography enlarged
Klappentext zu „Continuous Martingales and Brownian Motion “
From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..."Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.
Inhaltsverzeichnis zu „Continuous Martingales and Brownian Motion “
0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.- VIII. Girsanov's Theorem and First Applications.- IX. Stochastic Differential Equations.- X. Additive Functionals of Brownian Motion.- XI. Bessel Processes and Ray-Knight Theorems.- XII. Excursions.- XIII. Limit Theorems in Distribution.-1. Gronwall's Lemma.-
2. Distributions.-
3. Convex Functions.-
4. Hausdorff Measures and Dimension.-
5. Ergodic Theory.-
6. Probabilities on Function Spaces.-
7. Bessel Functions.-
8. Sturm-Liouville Equation.- Index of Notation.- Index of Terms.- Catalogue.
Bibliographische Angaben
- Autoren: Daniel Revuz , Marc Yor
- 2010, 3rd ed. 1999. Corr. 3rd printing, XIII, 602 Seiten, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642084001
- ISBN-13: 9783642084003
Sprache:
Englisch
Pressezitat
This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992) From the reviews of the third edition:
"The authors have revised the second edition of their fundamental and impressive monograph on Brownian motion and continuous martingales ... . The presentation of this book is unique in the sense that a concise and well-written text is complemented by a long series of detailed exercises. ... This third edition contains some additional exercises related to recent advances in the subject. ... is a valuable update of this basic reference book, which has been very helpful for researchers and students ... ." (David Nualart, Zentralblatt MATH, Vol. 1087, 2006)
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