  We consider the problem of optimal stopping for a one-dimensional diffusion
process. Two classes of admissible stopping times are considered. The first
class consists of all nonanticipating stopping times that take values in
[0,\infty], while the second class further restricts the set of allowed values
to the discrete grid {nh:n=0,1,2,...,\infty} for some parameter h>0. The value
functions for the two problems are denoted by V(x) and V^h(x), respectively. We
identify the rate of convergence of V^h(x) to V(x) and the rate of convergence
of the stopping regions, and provide simple formulas for the rate coefficients.
