Continuous Martingales and Brownian Motion

3rd Auflage 1999
ISBN: 978-3-540-64325-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 293, 602 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1098 g

Reihe: Grundlehren der mathematischen Wissenschaften

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.

Zielgruppe

Research

Autoren/Hrsg.

Yor, Marc

Revuz, Daniel

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.