Random Times & Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) by Roger Mansuy & Marc Yor
English | 2006 | ISBN: 3540294074 | 162 pages | PDF | 1,3 MB
In November 2004, M. Yor & 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 r&om time; martingales that vanish on the zero set of Brownian motion; the Azema-Emery martingales & 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 & main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers & graduate students working in stochastic calculus & excursion theory, & more broadly to mathematicians acquainted with the basics of Brownian motion.