Random Times and Enlargements of Filtrations in a Brownian Setting / by Roger Mansuy, Marc Yor.

Format:

Book

Author/Creator:

Mansuy, Roger, author.

Yor, Marc, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1873.

Lecture Notes in Mathematics, 0075-8434 ; 1873

Language:

English

Subjects (All):

Distribution (Probability theory).

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (XIII, 158 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540324164

Access Restriction:

Restricted for use by site license.