Measure changes with extinction

Details Measure changes with extinction Measure changes with extinction

2008-11-11

arxiv.org/abs/0811.1696v2

Mathematics

Probability

6 pages; corrected typo, shortened proof of Theorem 6

Scientific paper

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).

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