How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?

Ashkan Nikeghbali

Published 2005-05-23Version 1

This note deals with the question: what remains of the Burkholder-Davis-Gundy inequalities when stopping times $T$ are replaced by arbitrary random times $\rho $? We prove that these inequalities still hold when $T$ is a pseudo-stopping time and never holds for ends of predictable sets.