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arXiv:math/0505316 [math.PR]AbstractReferencesReviewsResources

Non Stopping Times and Stopping Theorems

Ashkan Nikeghbali

Published 2005-05-15, updated 2007-08-02Version 2

Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some families of martingales with remarkable properties. We also investigate, in the Brownian setting, the relationships between a given random time and the underlying Brownian Motion in the progressively enlarged filtration with respect to this random time.

Comments: Typos corrected. Close to the published version
Journal: Stochastic Processes and their applications; 117 (4)- p.457-475 (2007)
Categories: math.PR
Subjects: 05C38, 15A15, 15A18
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