On the distance between ⟨X⟩ and in the space of continuous BMO-martingales
Litan Yan, Norihiko Kazamaki (2005)
Studia Mathematica
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Let X = (Xₜ,ℱₜ) be a continuous BMO-martingale, that is, , where the supremum is taken over all stopping times T. Define the critical exponent b(X) by , where the supremum is taken over all stopping times T. Consider the continuous martingale q(X) defined by . We use q(X) to characterize the distance between ⟨X⟩ and the class of all bounded martingales in the space of continuous BMO-martingales, and we show that the inequalities hold for every continuous BMO-martingale X. ...