Random times and enlargements of filtrations in a Brownian setting

書誌事項

Random times and enlargements of filtrations in a Brownian setting

Roger Mansuy, Marc Yor

(Lecture notes in mathematics, 1873)

Springer, c2006

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注記

University lectures in Colombia University, between the 10th and the 25th of November 2004

Includes bibliographical references (p. [141]-155) and index

内容説明・目次

内容説明

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 Azema-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.

目次

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 Azema 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.

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