Non Stopping Times and Stopping Theorems

Details Non Stopping Times and Stopping Theorems Non Stopping Times and Stopping Theorems

2005-05-15

arxiv.org/abs/math/0505316v2

Stochastic Processes and their applications; 117 (4)- p.457-475 (2007)

Mathematics

Probability

Typos corrected. Close to the published version

Scientific paper

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.

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