XI: 25, 383-389, LNM 581 (1977)
DOLÉANS-DADE, Catherine;
MEYER, Paul-André
Une caractérisation de $BMO$ (
Martingale theory)
Kazamaki gave in
1027 a criterion for a continuous martingale to belong to $BMO$, involving its stochastic exponential. This criterion is extended, though in a different form, to non-continuous local martingales: $M$ belongs to $BMO$ if and only if for $|\lambda|$ small enough, its stochastic exponential ${\cal E}(\lambda M)$ is a (positive) multiplicatively bounded process---a class of processes, which looked promising but did not attract attention
Comment: Related subjects occur in
1328. The reference to ``note VI'' on p.384 probably refers to an earlier preprint, and is no longer intelligible
Keywords: $BMO$,
Stochastic exponentials,
Martingale inequalitiesNature: Original
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