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A continuous local martingale $M$ is constant on an interval if $\langle M\rangle$ is

As you indicate, the basic hypothesis is stable under stopping, so we can take $M$ to be a bounded martingale. Let $S\le T$ be stopping times such that $\langle M\rangle_T = \langle M\rangle_S$. then $...
John Dawkins's user avatar
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A continuous local martingale $M$ is constant on an interval if $\langle M\rangle$ is

Yes, the quadratic variation is unique by the Doob-Meyer-decomposition. Since $M^2-\langle M\rangle$ is a local martingale for a local martingale $M$, it necessarily holds $\langle M \rangle ^{\tau_n}=...
user408858's user avatar
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