  The effects of sampling rate and total measurement time have been determined
for single-point measurements of step fluctuations within the context of
first-passage properties. Time dependent STM has been used to evaluate step
fluctuations on Ag(111) films grown on mica as a function of temperature
(300-410 K), on screw dislocations on the facets of Pb crystallites at 320K,
and on Al-terminated Si(111) over the temperature range 770K - 970K. Although
the fundamental time constant for step fluctuations on Ag and Al/Si varies by
orders of magnitude over the temperature ranges of measurement, no dependence
of the persistence amplitude on temperature is observed. Instead, the
persistence probability is found to scale directly with t/Dt where Dt is the
time interval used for sampling. Survival probabilities show a more complex
scaling dependence which includes both the sampling interval and the total
measurement time tm. Scaling with t/Dt occurs only when Dt/tm is a constant. We
show that this observation is equivalent to theoretical predictions that the
survival probability will scale as Dt/L^z, where L is the effective length of a
step. This implies that the survival probability for large systems, when
measured with fixed values of tm or Dt should also show little or no
temperature dependence.
