Continuous Martingales and Brownian Motion - Daniel Revuz, Marc Yor

Continuous Martingales and Brownian Motion

, (Autoren)

Buch | Softcover
XIII, 602 Seiten
2010 | 3. Softcover reprint of hardcover 3rd ed. 1999
Springer Berlin (Verlag)
978-3-642-08400-3 (ISBN)
139,09 inkl. MwSt
3rd edition: proofs have been streamlined, errors removed, new exercises added and the bibliography enlarged
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.

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.

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)

Erscheint lt. Verlag 1.12.2010
Reihe/Serie Grundlehren der mathematischen Wissenschaften
Zusatzinfo XIII, 602 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 926 g
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Bessel process • Brownian motion • ergodic theory • local time • Markov process • Martingale • Martingales • Stochastic Integration • Stochastic Processes
ISBN-10 3-642-08400-1 / 3642084001
ISBN-13 978-3-642-08400-3 / 9783642084003
Zustand Neuware
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