Daniel Revuz, Marc Yor

Continuous Martingales and Brownian Motion

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Grundlehren der mathematischen Wissenschaften 293
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-64325-8
• 3rd ed., 3rd corr. pr.
• Seitenzahl: 628
• Erscheinungstermin: 18. Dezember 1998
• Englisch
• Abmessung: 241mm x 160mm x 39mm
• Gewicht: 1151g
• ISBN-13: 9783540643258
• ISBN-10: 3540643257
• Artikelnr.: 04065381

Inhaltsangabe

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.

Rezensionen

Dieses Buch kann mit Recht als eines der zentralen Referenzwerke auf dem Gebiet der Brown'schen Bewegung und Fragestellungen, die damit in Zusammenhang stehen, gelten. Der Ruf der Autoren allein bürgt schon dafür, und das Buch selbst besticht durch eine klare und konzise Darstellung, die von klassischen Resultaten im Stil von Paul Lévy zu modernen Betrachtungsweisen führt. Besondere Erwähnung verdienen die eingestreuten Übungsaufgaben, die in idealer Weise die Präsentation der allgemeinen Theorie ergänzen. Internationale Mathematische Nachrichten, Nr. 184, August 2000.

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)