Random Times and Enlargements of Filtrations in a Brownian Setting

2006
ISBN: 978-3-540-29407-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1873, 158 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azéma-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration.

The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.

Zielgruppe

Research

Autoren/Hrsg.

Yor, Marc

Mansuy, Roger

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Physik Thermodynamik Oberflächen- und Grenzflächenphysik, Dünne Schichten
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Notation and Convention.- Stopping and Non-stopping Times.- On the Martingales which Vanish on the Set of Brownian Zeroes.- Predictable and Chaotic Representation Properties for Some Remarkable Martingales Including the Azéma and the Dunkl Martingales.- Unveiling the Brownian Path (or history) as the Level Rises.- Weak and Strong Brownian Filtrations.- Sketches of Solutions for the Exercises.