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Probability Theory and Related Fields

, Volume 136, Issue 4, pp 524–540 | Cite as

Enlargements of filtrations and path decompositions at non stopping times

  • Ashkan Nikeghbali
Article

Abstract

Azéma associated with an honest time L the supermartingale Open image in new window and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic processes and in particular in the theory of progressive enlargements of filtrations. In this paper, we shall give an additive characterization for these supermartingales, which in turn will naturally provide many examples of enlargements of filtrations. We combine this characterization with some arguments from both initial and progressive enlargements of filtrations to establish some path decomposition results, closely related to or reminiscent of Williams' path decomposition results. In particular, some of the fragments of the paths in our decompositions end or start with a new family of random times which are not stopping times, nor honest times.

Mathematics Subject Classification (2000)

05C38 15A15 05A15 15A18 

Key words or phrases

Progressive enlargements of filtrations Initial enlargements of filtrations Azéma's supermartingale General theory of stochastic processes Path decompositions Pseudo-stopping times 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.American Institute of MathematicsUniversity of RochesterUSA

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