Simon Harris, Matthew Roberts
Published 2008-11-11, updated 2008-12-18Version 2
We consider a change of measure by a martingale $Z_t$ and clarify that in general $1/Z_t$ is only a supermartingale under the changed measure. We then give a necessary and sufficient condition for the event that the limit of the martingale is zero to coincide with the event that the martingale hits zero in finite time (up to a set of zero probability).
Comments: 6 pages; corrected typo, shortened proof of Theorem 6
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