The odds theorem gives a unified answer
to a class
of stopping problems on sequences of independent indicator functions. The
success
probability of the optimal rule is known to be larger than $Re^{-R}$,
where R defined in the theorem satisfies $R\ge 1$ in the more
interesting case.
The following findings strengthen this result by showing that
$1/e$ is then a lower bound. Knowing that
this is the best
possible uniform lower bound motivates this addendum.
Publié le : 2003-10-14
Classification:
Odds algorithm,
secretary problem,
group interviews,
investment problems,
1/e,
uniform lower bound,
60G40
@article{1068646368,
author = {Bruss, F. Thomas},
title = {A note on bounds for the odds theorem of optimal stopping},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1859-1961},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646368}
}
Bruss, F. Thomas. A note on bounds for the odds theorem of optimal stopping. Ann. Probab., Tome 31 (2003) no. 1, pp. 1859-1961. http://gdmltest.u-ga.fr/item/1068646368/