A new characterization of excessive functions for arbitrary one–dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as “the smallest nonnegative… (More)

@inproceedings{Dayanik2003OnTO,
title={On the Optimal Stopping Problem for One–dimensional Diffusions},
author={Savas Dayanik and Ioannis Karatzas},
year={2003}
}