= Bichteler-Dellacherie theorem
{c}
= Good integrator characterization of semimartingales
{synonym}
An adapted <càdlàg process> is a <semimartingale> exactly when it is a good integrator: on each finite horizon, for every sequence of bounded <elementary predictable processes with stopping-time intervals> $H^n$ whose deterministic uniform bounds tend to zero, the elementary terminal integrals $(H^n\mathbin\cdot X)_T$ tend to zero in <probability>. The elementary integral is a finite sum of measurable coefficients times subsequent increments; the characterization says precisely when this operation extends continuously to stochastic integration. The theorem is used here as a standard characterization, not proved from first principles.
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