测量灭绝的变化
Measure changes with extinction
摘要：
本文考虑了鞅$Z_t$的测度变换，并阐明了一般情况下$1/Z_t$只是变换测度下的上鞅.然后，我们给出了一个充要条件，使鞅的极限为零的事件与鞅在有限时间内（直到一个概率为零的集合）达到零的事件重合。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
