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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75287This note deals with the question: what remains of the Burkholder-Davis-Gundy inequalities when stopping times $T$ are replaced by arbitrary random times $ρ$? We prove that these inequalities still hold when $T$ is a pseudo-stopping time and never holds for ends of predictable sets.Probability05C38, 15A15,15A18How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?text