Measure changes with extinction
Probability
2008-12-18 v2
Abstract
We consider a change of measure by a martingale and clarify that in general 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).
Keywords
Cite
@article{arxiv.0811.1696,
title = {Measure changes with extinction},
author = {Simon Harris and Matthew Roberts},
journal= {arXiv preprint arXiv:0811.1696},
year = {2008}
}
Comments
6 pages; corrected typo, shortened proof of Theorem 6