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

Mathematics – Probability

Scientific paper

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Scientific paper

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.

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