How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?
Ashkan Nikeghbali
Abstract
This 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.
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